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 A260422 a(1) = 1, a(2n) = A205783(1+a(n)), a(2n+1) = A206074(a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q. 5
 1, 4, 2, 9, 7, 6, 3, 16, 23, 14, 17, 12, 13, 8, 5, 27, 47, 36, 71, 24, 41, 28, 53, 21, 31, 22, 37, 15, 19, 10, 11, 42, 81, 70, 149, 54, 109, 106, 239, 38, 73, 62, 127, 44, 83, 80, 171, 34, 67, 48, 91, 35, 69, 56, 113, 26, 43, 32, 59, 18, 25, 20, 29, 63, 131, 122, 271, 105, 233, 216, 477, 82, 173, 159, 353, 155, 347, 345, 787, 57 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence can be represented as a binary tree. Each left hand child is produced as A205783(1+n), and each right hand child as A206074(n), when the parent contains n: | ...................1................... 4 2 9......../ \........7 6......../ \........3 / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ 16 23 14 17 12 13 8 5 27 47 36 71 24 41 28 53 21 31 22 37 15 19 10 11 etc. LINKS Antti Karttunen, Table of n, a(n) for n = 1..8192 Index entries for sequences that are permutations of the natural numbers FORMULA a(1) = 1, a(2n) = A205783(1+a(n)), a(2n+1) = A206074(a(n)). As a composition of related permutations: a(n) = A260423(A246378(n)). a(n) = A260425(A246202(n)). PROG (PARI) uplim = (2^21) + (2^20); v206074 = vector(uplim); v205783 = vector(uplim); v205783[1] = 1; isA206074(n) = polisirreducible(Pol(binary(n))); i=0; j=1; n=2; while((n < uplim), if(!(n%65536), print1(n, ", ")); if(isA206074(n), i++; v206074[i] = n, j++; v205783[j] = n); n++); print(n); A260422(n) = if(1==n, 1, if(0==(n%2), v205783[1+A260422(n/2)], v206074[A260422((n-1)/2)])); for(n=1, 8192, write("b260422.txt", n, " ", A260422(n))); CROSSREFS Inverse: A260421. Related permutations: A246202, A246378, A260423, A260425. Cf. A205783, A206074. Differs from A246378 for the first time at n=16, where a(16)=27, while A246378(16)=26. Sequence in context: A213781 A257730 A246378 * A237126 A246380 A200639 Adjacent sequences: A260419 A260420 A260421 * A260423 A260424 A260425 KEYWORD nonn,tabf AUTHOR Antti Karttunen, Jul 25 2015 STATUS approved

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Last modified September 18 20:09 EDT 2024. Contains 376002 sequences. (Running on oeis4.)