A260425 - OEIS

%I #16 Jul 27 2015 22:13:04

%S 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,

%T 32,35,42,51,23,60,38,20,46,49,31,52,63,76,43,36,92,57,33,68,17,74,48,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A260425/b260425.txt">Table of n, a(n) for n = 1..4244</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F 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))).

%F As a composition of related permutations:

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

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

%o (PARI)

%o allocatemem(234567890);

%o vecsize = (2^24)-4;

%o uplim = 2^25;

%o v091226 = vector(vecsize); A091226 = n -> v091226[n];

%o A091245(n) = ((n-A091226(n))-1);

%o v206074 = vector(vecsize); A206074 = n -> v206074[n];

%o v205783 = vector(vecsize); A205783 = n -> v205783[n];

%o isA014580(n) = polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from _Charles R Greathouse IV_

%o isA206074(n) = polisirreducible(Pol(binary(n)));

%o 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);

%o A260425(n) = if(1==n, 1, if(isA014580(n), A206074(A260425(A091226(n))), A205783(1+A260425(A091245(n)))));

%o for(n=1, 4244, write("b260425.txt", n, " ", A260425(n)));

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

%Y Inverse: A260426.

%Y Related permutations: A246201, A245704, A260422, A260423.

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

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 26 2015