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A305417
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Permutation of natural numbers: a(0) = 1, a(2n) = A305421(a(n)), a(2n+1) = 2*a(n).
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4
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1, 2, 3, 4, 7, 6, 5, 8, 11, 14, 9, 12, 21, 10, 15, 16, 13, 22, 29, 28, 49, 18, 27, 24, 69, 42, 63, 20, 107, 30, 17, 32, 19, 26, 23, 44, 35, 58, 39, 56, 127, 98, 83, 36, 151, 54, 45, 48, 81, 138, 207, 84, 475, 126, 65, 40, 743, 214, 189, 60, 273, 34, 51, 64, 25, 38, 53, 52, 121, 46, 57, 88, 173, 70, 101, 116, 233, 78, 105, 112, 199, 254, 129
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OFFSET
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0,2
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COMMENTS
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This is GF(2)[X] analog of A005940, but note the indexing: here the domain starts from 0, although the range excludes zero.
This sequence can be represented as a binary tree. Each child to the left is obtained by applying A305421 to the parent, and each child to the right is obtained by doubling the parent:
1
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...................2...................
3 4
7......../ \........6 5......../ \........8
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
11 14 9 12 21 10 15 16
13 22 29 28 49 18 27 24 69 42 63 20 107 30 17 32
Sequence A305427 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(2n) = A305421(a(n)), a(2n+1) = 2*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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