Problem 54660. Generate the Figure-Figure sequence

Created by ChrisR

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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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Last Solution submitted on Dec 07, 2025

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GeeTwo on 25 Apr 2024

The description indicates that this is just the series of odd integers, because 2 will never be in a. To achieve the next number being 7, you need to also establish list b, being the numbers added, and that the next a is the previous a plus the smallest natural number neither in a nor b.

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Problem 54660. Generate the Figure-Figure sequence

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Problem 54660. Generate the Figure-Figure sequence

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Last 200 Solutions

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