{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":47073,"title":"Find the nth Fibbinary number","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 308.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 154.375px; transform-origin: 407px 154.375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.625px; text-align: left; transform-origin: 384px 31.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.117px 7.91667px; transform-origin: 255.117px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 0, 1, 2, 4, 5, 8, 9, and 10 form the first eight elements (i.e., elements \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a_0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 7.91667px; transform-origin: 9.71667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABJ0lEQVRYhe2WUY3DMAyGPw5lMAIlEARFMAZhUAajEAyFEA6lUAylsHuYc3Ozutmm5aaT8kl+aGz5d+y0KTQajUaj8SV6wAMj4GTNyXNfUzQCi4g7IAAzcBU71RA+S/IF6DLfVfn+VFiLXz4tPKjkbsd/KvjfpgNWSTwZMakrK9uuBFXUnhULHVWwdYqj+GNW9CKFucxm7PFtSLuOht+p4ka17kXYyhlKwlZiTaTcGU06P0MpULd8L9hz70w+b4vwbOyR+Jnb3Ca2YwnYXUKErYO7oVfiUartJHk6MGnnQewoccpnnYUH0s60TdzbtmbrR1wk7pnx/DJw263n8bv9ymWyYL81VUlfQf8NcU/FG6/ELPbSvD9BavnRK1iNdPFU+8NpNBr/gx+twmvaJTM4bAAAAABJRU5ErkJggg==\" alt=\"a_7\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.683px 7.91667px; transform-origin: 102.683px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) of the Fibbinary sequence. The name is a portmanteau that arose because of connections to Fibonacci numbers and binary numbers. The connection to Fibonacci numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"F(k)\" style=\"width: 32.5px; height: 19px;\" width=\"32.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.7167px 7.91667px; transform-origin: 37.7167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis that if the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/47058-determine-the-zeckendorf-expansion-of-a-number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eZeckendorf expansion\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 7.91667px; transform-origin: 9.71667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 7.91667px; transform-origin: 8.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.625px; text-align: left; transform-origin: 384px 10.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = F(k_1) + F(k_2) + \\ldots + F(k_m)\" style=\"width: 199px; height: 20px;\" width=\"199\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 7.91667px; transform-origin: 13.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 26px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13px; text-align: left; transform-origin: 384px 13px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a_n = 2^{k_1-2}+2^{k_2-2}+\\ldots+2^{k_m-2}\" style=\"width: 192px; height: 26px;\" width=\"192\" height=\"26\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357.083px 7.91667px; transform-origin: 357.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe connection to binary numbers is that the binary representations of the Fibbinary numbers have no adjacent 1s. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.625px; text-align: left; transform-origin: 384px 10.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 7.91667px; transform-origin: 42.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABJ0lEQVRYhe2WUY3DMAyGPw5lMAIlEARFMAZhUAajEAyFEA6lUAylsHuYc3Ozutmm5aaT8kl+aGz5d+y0KTQajUaj8SV6wAMj4GTNyXNfUzQCi4g7IAAzcBU71RA+S/IF6DLfVfn+VFiLXz4tPKjkbsd/KvjfpgNWSTwZMakrK9uuBFXUnhULHVWwdYqj+GNW9CKFucxm7PFtSLuOht+p4ka17kXYyhlKwlZiTaTcGU06P0MpULd8L9hz70w+b4vwbOyR+Jnb3Ca2YwnYXUKErYO7oVfiUartJHk6MGnnQewoccpnnYUH0s60TdzbtmbrR1wk7pnx/DJw263n8bv9ymWyYL81VUlfQf8NcU/FG6/ELPbSvD9BavnRK1iNdPFU+8NpNBr/gx+twmvaJTM4bAAAAABJRU5ErkJggg==\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.975px 7.91667px; transform-origin: 148.975px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 10. The Zeckendorf expansion of 7 is 2+5, or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"F(3)+F(5)\" style=\"width: 79.5px; height: 19px;\" width=\"79.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"10=2^{3-2}+2^{5-2} = 2+8\" style=\"width: 155px; height: 19.5px;\" width=\"155\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 210.442px 7.91667px; transform-origin: 210.442px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAlso, the binary expansion of 10 is 1010, which has no adjacent 1s. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.1px 7.91667px; transform-origin: 83.1px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.7333px 7.91667px; transform-origin: 65.7333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth Fibbinary number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Fibbinary(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 0;\r\ny_correct = 0;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 4;\r\ny_correct = 5;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 7;\r\ny_correct = 10;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 77;\r\ny_correct = 321;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 777;\r\ny_correct = 9282;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 5000;\r\ny_correct = 140562;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 7777;\r\ny_correct = 278597;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 77777;\r\ny_correct = 8455236;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 100000;\r\ny_correct = 9704021;\r\nassert(isequal(Fibbinary(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-25T02:19:28.000Z","updated_at":"2020-10-27T04:39:32.000Z","published_at":"2020-10-25T03:48:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 0, 1, 2, 4, 5, 8, 9, and 10 form the first eight elements (i.e., elements \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_7\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) of the Fibbinary sequence. The name is a portmanteau that arose because of connections to Fibonacci numbers and binary numbers. The connection to Fibonacci numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F(k)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis that if the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/47058-determine-the-zeckendorf-expansion-of-a-number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eZeckendorf expansion\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = F(k_1) + F(k_2) + \\\\ldots + F(k_m)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = F(k_1) + F(k_2) + \\\\ldots + F(k_m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_n = 2^{k_1-2}+2^{k_2-2}+\\\\ldots+2^{k_m-2}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n = 2^{k_1-2}+2^{k_2-2}+\\\\ldots+2^{k_m-2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe connection to binary numbers is that the binary representations of the Fibbinary numbers have no adjacent 1s. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 10. The Zeckendorf expansion of 7 is 2+5, or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F(3)+F(5)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(3)+F(5)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"10=2^{3-2}+2^{5-2} = 2+8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10=2^{3-2}+2^{5-2} = 2+8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlso, the binary expansion of 10 is 1010, which has no adjacent 1s. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth Fibbinary number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":47073,"title":"Find the nth Fibbinary number","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 308.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 154.375px; transform-origin: 407px 154.375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.625px; text-align: left; transform-origin: 384px 31.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.117px 7.91667px; transform-origin: 255.117px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 0, 1, 2, 4, 5, 8, 9, and 10 form the first eight elements (i.e., elements \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a_0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 7.91667px; transform-origin: 9.71667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABJ0lEQVRYhe2WUY3DMAyGPw5lMAIlEARFMAZhUAajEAyFEA6lUAylsHuYc3Ozutmm5aaT8kl+aGz5d+y0KTQajUaj8SV6wAMj4GTNyXNfUzQCi4g7IAAzcBU71RA+S/IF6DLfVfn+VFiLXz4tPKjkbsd/KvjfpgNWSTwZMakrK9uuBFXUnhULHVWwdYqj+GNW9CKFucxm7PFtSLuOht+p4ka17kXYyhlKwlZiTaTcGU06P0MpULd8L9hz70w+b4vwbOyR+Jnb3Ca2YwnYXUKErYO7oVfiUartJHk6MGnnQewoccpnnYUH0s60TdzbtmbrR1wk7pnx/DJw263n8bv9ymWyYL81VUlfQf8NcU/FG6/ELPbSvD9BavnRK1iNdPFU+8NpNBr/gx+twmvaJTM4bAAAAABJRU5ErkJggg==\" alt=\"a_7\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.683px 7.91667px; transform-origin: 102.683px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) of the Fibbinary sequence. The name is a portmanteau that arose because of connections to Fibonacci numbers and binary numbers. The connection to Fibonacci numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"F(k)\" style=\"width: 32.5px; height: 19px;\" width=\"32.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.7167px 7.91667px; transform-origin: 37.7167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis that if the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/47058-determine-the-zeckendorf-expansion-of-a-number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eZeckendorf expansion\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 7.91667px; transform-origin: 9.71667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 7.91667px; transform-origin: 8.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.625px; text-align: left; transform-origin: 384px 10.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = F(k_1) + F(k_2) + \\ldots + F(k_m)\" style=\"width: 199px; height: 20px;\" width=\"199\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 7.91667px; transform-origin: 13.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 26px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13px; text-align: left; transform-origin: 384px 13px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a_n = 2^{k_1-2}+2^{k_2-2}+\\ldots+2^{k_m-2}\" style=\"width: 192px; height: 26px;\" width=\"192\" height=\"26\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357.083px 7.91667px; transform-origin: 357.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe connection to binary numbers is that the binary representations of the Fibbinary numbers have no adjacent 1s. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.625px; text-align: left; transform-origin: 384px 10.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 7.91667px; transform-origin: 42.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABJ0lEQVRYhe2WUY3DMAyGPw5lMAIlEARFMAZhUAajEAyFEA6lUAylsHuYc3Ozutmm5aaT8kl+aGz5d+y0KTQajUaj8SV6wAMj4GTNyXNfUzQCi4g7IAAzcBU71RA+S/IF6DLfVfn+VFiLXz4tPKjkbsd/KvjfpgNWSTwZMakrK9uuBFXUnhULHVWwdYqj+GNW9CKFucxm7PFtSLuOht+p4ka17kXYyhlKwlZiTaTcGU06P0MpULd8L9hz70w+b4vwbOyR+Jnb3Ca2YwnYXUKErYO7oVfiUartJHk6MGnnQewoccpnnYUH0s60TdzbtmbrR1wk7pnx/DJw263n8bv9ymWyYL81VUlfQf8NcU/FG6/ELPbSvD9BavnRK1iNdPFU+8NpNBr/gx+twmvaJTM4bAAAAABJRU5ErkJggg==\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.975px 7.91667px; transform-origin: 148.975px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 10. The Zeckendorf expansion of 7 is 2+5, or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"F(3)+F(5)\" style=\"width: 79.5px; height: 19px;\" width=\"79.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATYAAAAnCAYAAACFQWQjAAAF2ElEQVR4nO2d63GrMBCFTw904AbcgCtwBe7gduAO0oJroAT3kBZcg1vI/SHOsMECVrACiew3o4ln4ghYVker1SOA4ziO4ziO4ziO4ziO4zhO2ZwA/ANw737m4tJd4959PjLyWVmextdoAFxF/Sfj+h2nWm4AfhAa3av7/A3bRtJ0db66nz9dabvfHRH5nCx3w/rPAN7o7ZrjGo5TJSeERiFFrEVoIJaR23NQHxvlURviBcGuuWi6+mXUyw7qB8ePhh1nkn8IIiO5IDSOL6NrnBCiiti1f0Z+VztP5BXsG+Lvh52S1btznMNwRWgcQ8FbymmkLgro0YTthD5yegF4wM6W5IL4EP4OF7ZDckNwJq0jnRAc74k+x9Qm/H1pXBDun8M85s6uCXUMh425sI4Mc3FDsAnt+ca0j1zxO1/Jv9nCphS2lPe9N6n2LRE+Q4v+3X/DIGqnoNE4GqPIpLns/R6oo8EN+cJnslqWuec5IdjirfiuBWyEpTpwg98NLlbmBOQi6ngj/7Py/dWAhX33Rk6KDfOa1JdFI5IzQiP8wu8oZc6BGC288Tn7x8SsdQI9Jxw+tt3nCz57wqnnOaNfjrDV7NoLZXce9KkHgj0vCPaTHahWmJn7emS50wCHwKWLAbG0716wvdxGfs9gI9nPpSgxAtAYg8YbczQmtt+oYznCVJTFZ2HOZw72NMPvxtZlTZUpu9GBLWE6wWKZCmdtxxyWQqUVqwbx3vsGvT3nOtlWeS8lYG1fLZY+InOpY3rDAGqVr2uFTU6Ljxn2jO0il7XcEBrMlJDIXlDzUjkcl3UyAtSWsfs5K+53CZY9/APTDWo4QaDhiU9h+4LenlP3c0MQg1rIYV8Nlj5C0ZpaXiNHhovRClur/B6/U/qs3QPjAk1k/k3zUu/IE60yJ5FjnZWl034r6uECXK3TMrlszRmh8dcwsiA57KvB0kek+I69V46WVkWdWmGTsy9TyHxTTU4Tg7aJ5RRjMJKwhMnimKjNCbOGrXMy9A9tx5djZnQs+uVWq5pJta8Gax+RGjFMBTFX/8bKjlwjbFJlU4St9pXcjNiGTsJJBkmDYBvLhsFILdawuUd1LVsLGyMK6dAN+pyYJEdOkZHa0Dcb9An5monZdy3WPiJ30MgVFlyUbjI60QibHBenCJu2p5X1rynWPTudZChisle8IYhZG/neWuTwP1YskrlbChsnA4ZLOGRulja9wz6nKGfuYyVFREv02TH7riWHjwzF7Y1g/7kJNDWpwjY31JJ5qZqFjVFqLKRv0EdMuU7c4FKSsWIlolsKGyegYtHE8KSUHPcjT/SIlZT3WKLPTtl3Dbl8hNGztIdZKidV2OYSubK+WtazxXjAYJxfAVsK2wv1JexrIpd9c/nIBf1JK1LctDntSUoYipYGDW49tNyDuVXqmmIxw3ZH2rY9J4019t3DR4bR5RWfQ9NV4qYRtgb6B6h98oCTACWv7k+hBGE7UkdRImvtu7WPcMfPMM3DyTKTYal2uQfVVCtsW+zxs4aGPYqoacg9FGUexUUtD1vY19pHmFeL3fNQ3BZHbUsW6E5djAJY2wzTXxQ1IK+wHVnUSvDZrexr6SNyBnzqpJfV9lmypWpsrZZc75YiEHs7iVbUjpj0ziVsmkZXsz339tkt7WvpI9Jumg0B2YUNSNsEX9M/yHhgfrbXakFsaeQQtqmFxZIWdeZh92Zr+1r6iMzXTy1m53cW33+KsEm1jfUGtR1bBPTLOnhsUaxwD2hNYq3FWtjY6Lh6fKy0KH8/cYnsYV9rH+FhEWPBxNjkQhJyRkSzHWjsILgaD5rkPWtKTadApGDdG8f+y1SO/NJfZC/75ur8YqM/DrEXLV05IQhQbHvJA/MGYY/wQn+sTI4tRTmZOzl3WGrfHD2GpdOmNLqjRsA52cu+ufKwPNLrjd9HTZltq3L+LnSm2pbmONvhPuI4juM4juM4juM4juM4juM4juM4juM4juM4juM4juM4R+U/x8K/vnR0grkAAAAASUVORK5CYII=\" alt=\"10=2^{3-2}+2^{5-2} = 2+8\" style=\"width: 155px; height: 19.5px;\" width=\"155\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 210.442px 7.91667px; transform-origin: 210.442px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAlso, the binary expansion of 10 is 1010, which has no adjacent 1s. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.1px 7.91667px; transform-origin: 83.1px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.7333px 7.91667px; transform-origin: 65.7333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth Fibbinary number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Fibbinary(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 0;\r\ny_correct = 0;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 4;\r\ny_correct = 5;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 7;\r\ny_correct = 10;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 77;\r\ny_correct = 321;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 777;\r\ny_correct = 9282;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 5000;\r\ny_correct = 140562;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 7777;\r\ny_correct = 278597;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 77777;\r\ny_correct = 8455236;\r\nassert(isequal(Fibbinary(n),y_correct))\r\n\r\n%%\r\nn = 100000;\r\ny_correct = 9704021;\r\nassert(isequal(Fibbinary(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-25T02:19:28.000Z","updated_at":"2020-10-27T04:39:32.000Z","published_at":"2020-10-25T03:48:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 0, 1, 2, 4, 5, 8, 9, and 10 form the first eight elements (i.e., elements \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_7\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) of the Fibbinary sequence. The name is a portmanteau that arose because of connections to Fibonacci numbers and binary numbers. The connection to Fibonacci numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F(k)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis that if the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/47058-determine-the-zeckendorf-expansion-of-a-number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eZeckendorf expansion\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = F(k_1) + F(k_2) + \\\\ldots + F(k_m)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = F(k_1) + F(k_2) + \\\\ldots + F(k_m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_n = 2^{k_1-2}+2^{k_2-2}+\\\\ldots+2^{k_m-2}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n = 2^{k_1-2}+2^{k_2-2}+\\\\ldots+2^{k_m-2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe connection to binary numbers is that the binary representations of the Fibbinary numbers have no adjacent 1s. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 10. The Zeckendorf expansion of 7 is 2+5, or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F(3)+F(5)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(3)+F(5)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"10=2^{3-2}+2^{5-2} = 2+8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10=2^{3-2}+2^{5-2} = 2+8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlso, the binary expansion of 10 is 1010, which has no adjacent 1s. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth Fibbinary number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"zeckendorf\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"zeckendorf\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"zeckendorf\"","","\"","zeckendorf","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f234adb51e0\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f234adb5140\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f234adb4880\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f234adb5460\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f234adb53c0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f234adb5320\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f234adb5280\u003e":"tag:\"zeckendorf\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f234adb5280\u003e":"tag:\"zeckendorf\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"zeckendorf\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"zeckendorf\"","","\"","zeckendorf","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f234adb51e0\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f234adb5140\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f234adb4880\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f234adb5460\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f234adb53c0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f234adb5320\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f234adb5280\u003e":"tag:\"zeckendorf\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f234adb5280\u003e":"tag:\"zeckendorf\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":47073,"difficulty_rating":"medium"}]}}