Problem 47058. Determine the Zeckendorf expansion of a number

Created by ChrisR

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<div 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; "><div style="block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; "><div style="block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 14px 8.05px; transform-origin: 14px 8.05px; unicode-bidi: normal; "><span style="">The </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Goldbach%27s_conjecture"><span style=""><span style="">Goldbach conjecture</span></span></a><span 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: 294.442px 8.05px; transform-origin: 294.442px 8.05px; unicode-bidi: normal; "><span style=""> deals with expressing integers as sums of primes. One might also seek to express integers as sums of other numbers, such as the </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Fibonacci_number"><span style=""><span style="">Fibonacci numbers</span></span></a><span 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: 199.892px 8.05px; transform-origin: 199.892px 8.05px; unicode-bidi: normal; "><span style="">, which begin 0, 1, 1, 2, 3, 5, 8, 13, 21... For example, 26 can be written as 13+8+5 or 21+3+2. </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Zeckendorf%27s_theorem"><span style=""><span style="">Zeckendorf</span></span></a><span 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: 255.608px 8.05px; transform-origin: 255.608px 8.05px; unicode-bidi: normal; "><span style=""> (and Lekkerkerker before him) showed that every positive integer can be uniquely expressed as the sum of </span></span><span 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: 50.9667px 8.05px; transform-origin: 50.9667px 8.05px; unicode-bidi: normal; "><span style="font-style: italic; ">non-consecutive</span></span><span 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: 196.242px 8.05px; transform-origin: 196.242px 8.05px; unicode-bidi: normal; "><span style=""> Fibonacci numbers. The Zeckendorf expansion for 26 is 21+5. </span></span></div><div style="block-size: 42px; 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 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 372.5px 8.05px; transform-origin: 372.5px 8.05px; unicode-bidi: normal; "><span style="">Write a function to determine the Zeckendorf expansion of the input number. In particular, output in decreasing order the Fibonacci numbers to be used in the sum.</span></span></div></div></div>

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Problem 47058. Determine the Zeckendorf expansion of a number

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