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 A305427 Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = 2*a(n), a(2n+1) = A305421(a(n)). 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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:                                      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 etc. Sequence A305417 is obtained by scanning the same tree level by level from right to left. LINKS Antti Karttunen, Table of n, a(n) for n = 0..16383 FORMULA a(0) = 1, a(1) = 2, a(2n) = 2*a(n), a(2n+1) = A305421(a(n)). a(n) = A305417(A054429(n)). PROG (PARI) A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2)); A305420(n) = { my(k=1+n); while(!A091225(k), k++); (k); }; 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); }; A305427(n) = if(n<=1, (1+n), if(!(n%2), 2*A305427(n/2), A305421(A305427((n-1)/2)))); CROSSREFS Cf. A305428 (inverse), A305417 (mirror image). Cf. A305421. Cf. also A091202, A163511. Sequence in context: A246367 A048167 A207790 * A269375 A135141 A098709 Adjacent sequences:  A305424 A305425 A305426 * A305428 A305429 A305430 KEYWORD nonn,tabf AUTHOR Antti Karttunen, Jun 10 2018 STATUS approved

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Last modified April 5 20:58 EDT 2020. Contains 333260 sequences. (Running on oeis4.)