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The infinite sequence begins with 0, 2, 1, 6, 3, 5, 4, 14, 7, 9, 8, 13, 10, 12, 11, 30, …

The full sequence contains every positive integer (and zero) exactly once.

What are the next 16 items of the sequence and why?

Hint 1: (includes the next 8 numbers in the sequence)

0,2,1,6,3,5,4,14,7,9,8,13,10,12,11,30,15,17,16,21,18,20,19,29

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    $\begingroup$ How many items? And does the \ and / have to do anything with it? $\endgroup$ Commented Mar 18 at 6:07
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    $\begingroup$ @user5127 Edited to extend the sequence and ask for 16 items. The / and \ are to differentiate the title from other number sequence puzzles, but are also on-theme. $\endgroup$ Commented Mar 18 at 6:40

1 Answer 1

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Answer:

..., 15, 17, 16, 21, 18, 20, 19, 29, 22, 24, 23, 28, 25, 27, 26, 62, ...

Explanation:

For each n ≥ 0, given the first 2n-1 numbers in the sequence, the next number is 2n+1-2, and the next 2n-1 numbers are the first 2n-1 numbers plus 2n-1. Now we have 2n+1-1 numbers, and we repeat for n+1. It is not too hard to check that we generate all non-negative integers exactly once in this process.

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