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.

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

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