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A233276
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a(0)=0, a(1)=1, after which a(2n) = A005187(1+a(n)), a(2n+1) = A055938(a(n)).
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16
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0, 1, 3, 2, 7, 6, 4, 5, 15, 14, 11, 13, 8, 9, 10, 12, 31, 30, 26, 29, 22, 24, 25, 28, 16, 17, 18, 20, 19, 21, 23, 27, 63, 62, 57, 61, 50, 55, 56, 60, 42, 45, 47, 51, 49, 52, 54, 59, 32, 33, 34, 36, 35, 37, 39, 43, 38, 40, 41, 44, 46, 48, 53, 58, 127, 126, 120
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OFFSET
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0,3
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COMMENTS
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This permutation is obtained by "entangling" even and odd numbers with complementary pair A005187 & A055938, meaning that it can be viewed as a binary tree. Each child to the left is obtained by applying A005187(n+1) to the parent node containing n, and each child to the right is obtained as A055938(n):
0
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...................1...................
3 2
7......../ \........6 4......../ \........5
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
15 14 11 13 8 9 10 12
31 30 26 29 22 24 25 28 16 17 18 20 19 21 23 27
etc.
For n >= 1, A256991(n) gives the contents of the immediate parent node of the node containing n, while A070939(n) gives the total distance to 0 from the node containing n, with A256478(n) telling how many of the terms encountered on that journey are terms of A005187 (including the penultimate 1 but not the final 0 in the count), while A256479(n) tells how many of them are terms of A055938.
Permutation A233278 gives the mirror image of the same tree.
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LINKS
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FORMULA
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a(0)=0, a(1)=1, and thereafter, a(2n) = A005187(1+a(n)), a(2n+1) = A055938(a(n)).
As a composition of related permutations:
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PROG
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(Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library)
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CROSSREFS
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Cf. also A070939 (the binary width of both n and a(n)).
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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Name changed and the illustration of binary tree added by Antti Karttunen, Apr 19 2015
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STATUS
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approved
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