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A305427
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Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = 2*a(n), a(2n+1) = A305421(a(n)).
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4
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1, 2, 4, 3, 8, 5, 6, 7, 16, 15, 10, 21, 12, 9, 14, 11, 32, 17, 30, 107, 20, 63, 42, 69, 24, 27, 18, 49, 28, 29, 22, 13, 64, 51, 34, 273, 60, 189, 214, 743, 40, 65, 126, 475, 84, 207, 138, 81, 48, 45, 54, 151, 36, 83, 98, 127, 56, 39, 58, 35, 44, 23, 26, 19, 128, 85, 102, 1911, 68, 819, 546, 4113, 120, 455, 378, 3253, 428, 1833, 1486, 925, 80
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OFFSET
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0,2
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COMMENTS
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Note the indexing: Domain starts from 0, while range starts from 1.
This is GF(2)[X] analog of A163511.
This sequence can be represented as a binary tree. Each child to the left is obtained by doubling the parent, and each child to the right is obtained by applying A305421 to the parent:
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...................2...................
4 3
8......../ \........5 6......../ \........7
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
16 15 10 21 12 9 14 11
32 17 30 107 20 63 42 69 24 27 18 49 28 29 22 13
etc.
Sequence A305417 is obtained by scanning the same tree level by level from right to left.
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LINKS
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FORMULA
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a(0) = 1, a(1) = 2, a(2n) = 2*a(n), a(2n+1) = A305421(a(n)).
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PROG
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(PARI)
A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
A305421(n) = { my(f = subst(lift(factor(Pol(binary(n))*Mod(1, 2))), x, 2)); for(i=1, #f~, f[i, 1] = Pol(binary(A305420(f[i, 1])))); fromdigits(Vec(factorback(f))%2, 2); };
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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