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A276442
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Permutation of natural numbers: a(1) = 1; a(2n) = A088359(a(n)), a(2n+1) = A087686(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001.
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6
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1, 3, 2, 6, 7, 5, 4, 11, 14, 13, 15, 10, 12, 9, 8, 20, 26, 25, 30, 23, 29, 28, 31, 19, 24, 22, 27, 18, 21, 17, 16, 37, 47, 46, 57, 44, 56, 55, 62, 41, 53, 52, 61, 50, 60, 59, 63, 36, 45, 43, 54, 40, 51, 49, 58, 35, 42, 39, 48, 34, 38, 33, 32, 70, 85, 84, 105, 82, 104, 103, 120, 79, 101, 100, 119, 98, 118, 117, 126, 75, 95, 94
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OFFSET
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1,2
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COMMENTS
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This sequence can be represented as a binary tree. Each left hand child is produced as A088359(n), and each right hand child as A087686(1+n), when their parent contains n:
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...................1...................
3 2
6......../ \........7 5......../ \........4
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
11 14 13 15 10 12 9 8
20 26 25 30 23 29 28 31 19 24 22 27 18 21 17 16
etc.
As in the mirror image permutation A267112, the level k of the tree contains all numbers of binary width k like many other base-2 related permutations (A003188, A054429, A233278, etc). For a proof, see A267110, which gives the contents of each parent node (for a node containing n > 1).
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LINKS
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FORMULA
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a(1) = 1; after which, a(2n) = A088359(a(n)), a(2n+1) = A087686(1+a(n)).
As a composition of other permutations:
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PROG
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(Scheme)
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CROSSREFS
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KEYWORD
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nonn,base,tabf
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AUTHOR
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STATUS
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approved
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