A305423 - OEIS

%I #7 Jun 08 2018 13:52:52

%S 1,2,4,3,11,5,6,8,25,32,7,14,10,15,54,9,137,42,13,33,35,12,61,23,16,

%T 27,76,20,18,95,19,26,126,410,87,123,21,22,117,98,24,104,47,29,499,70,

%U 28,60,64,17,956,48,40,221,30,53,184,51,31,228,34,56,238,43,641,135,37,683,41,252,229,144,44,62,775,63,90,158,109,163,131,57

%N Permutation of natural numbers: a(n) = (A305421(n)+1)/2.

%H Antti Karttunen, <a href="/A305423/b305423.txt">Table of n, a(n) for n = 1..13106</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>

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

%F a(n) = (A305421(n)+1)/2.

%o (PARI)

%o A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));

%o A305420(n) = { my(k=1+n); while(!A091225(k),k++); (k); };

%o A305421(n) = { my(f = subst(lift(factor(Pol(binary(n))*Mod(1, 2))),x,2)); for(i=1,#f~,f[i,1] = Pol(binary(A305420(f[i,1])))); fromdigits(Vec(factorback(f))%2,2); };

%o A305423(n) = ((1+A305421(n))/2);

%Y Cf. A305424 (inverse).

%Y Cf. A014580, A091225, A304521.

%Y Cf. also A048673.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 08 2018