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

Author

Antti Karttunen, Jul 25 2015

Keywords

• nonn
• tabf

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

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.

Programs

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)));

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)).