Problem 54660. Generate the Figure-Figure sequence

• Created by ChrisR
• Appears in Sequences and Series VI

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After discussing Scott Kim’s FIGURE-FIGURE Figure (below) in Gödel, Escher, Bach, Douglas Hofstadter introduced an integer sequence a (say) generated by this rule: it starts with 1, and each later term equals the sum of the previous term in a and the latest term that is not already contained the sequence a.

For example, the second term in the sequence is 3 because the first number not in the sequence is 2, and 1+2 = 3. The third term is 7 because the next term not in a is 4 and 3+4 = 7.

Not only is the complement of the sequence a equal to the differences between the terms, but together the two sequences contain all positive integers.

Write a function that returns the nth term of the sequence.

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Solution Stats

71.43% Correct | 28.57% Incorrect

• 14 Solutions
• 10 Solvers

Last Solution submitted on Oct 22, 2024

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