A260425 a(1) = 1, a(A014580(n)) = A206074(a(n)), a(A091242(n)) = A205783(1+a(n)), where A014580(n) [resp. A091242(n)] give binary codes for n-th irreducible [resp. reducible] polynomial over GF(2), while A206074 and A205783 give similar codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

1, 2, 3, 4, 6, 8, 5, 9, 12, 15, 7, 10, 13, 16, 21, 26, 14, 18, 19, 22, 27, 34, 40, 24, 11, 30, 32, 35, 42, 51, 23, 60, 38, 20, 46, 49, 31, 52, 63, 76, 43, 36, 92, 57, 33, 68, 17, 74, 48, 78, 95, 114, 64, 54, 25, 135, 86, 50, 37, 102, 47, 28, 111, 72, 118, 140, 67, 165, 96, 82, 39, 195, 79, 128, 75, 56, 150, 70, 44

Offset: 1

Author

Antti Karttunen, Jul 26 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4244
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A260426.

Related permutations: A246201, A245704, A260422, A260423.

Cf. A014580, A091225, A091226, A091242, A091245, A205783, A206074.

Differs from A245704 for the first time at n=16, where a(16) = 26, while A245704(16) = 25.

Programs

PARI

allocatemem(234567890);
vecsize = (2^24)-4;
uplim = 2^25;
v091226 = vector(vecsize); A091226 = n -> v091226[n];
A091245(n) = ((n-A091226(n))-1);
v206074 = vector(vecsize); A206074 = n -> v206074[n];
v205783 = vector(vecsize); A205783 = n -> v205783[n];
isA014580(n) = polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
isA206074(n) = polisirreducible(Pol(binary(n)));
v091226[1] = 0; v205783[1] = 1; 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); if(isA014580(n), v091226[n] = v091226[n-1]+1, v091226[n] = v091226[n-1]); n++); print(n);
A260425(n) = if(1==n, 1, if(isA014580(n), A206074(A260425(A091226(n))), A205783(1+A260425(A091245(n)))));
for(n=1, 4244, write("b260425.txt", n, " ", A260425(n)));

Scheme

(definec (A260425 n) (cond ((<= n 1) n) ((= 1 (A091225 n)) (A206074 (A260425 (A091226 n)))) (else (A205783 (+ 1 (A260425 (A091245 n)))))))

Formula

a(1) = 1; for n > 1, if A091225(n) = 1 [when n is in A014580], then a(n) = A206074(a(A091226(n))), otherwise [when n is in A091242], a(n) = A205783(1+a(A091245(n))).

As a composition of related permutations:

a(n) = A260422(A246201(n)).

a(n) = A260423(A245704(n)).