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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..4244

Index entries for sequences that are permutations of the natural numbers

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)).

Prog

(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)))))))

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.

Sequence in context: A083197 A235262 A245704 * A352064 A277905 A257802

Adjacent sequences: A260422 A260423 A260424 * A260426 A260427 A260428

Keyword

nonn

Author

Antti Karttunen, Jul 26 2015

Status

approved