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%I #6 Jun 08 2018 13:52:57
%S 1,2,4,3,6,7,11,8,16,13,5,22,19,12,14,25,50,29,31,28,37,38,24,41,9,32,
%T 26,47,44,55,59,10,20,61,21,118,67,88,110,53,69,18,64,73,94,87,43,52,
%U 91,100,58,97,56,15,103,62,82,109,115,48,23,74,76,49,98,117,113,152,131,46,148,137,143,164,218,27,96,227,145,230,89,182,200
%N Permutation of natural numbers: a(n) = A305422(2*n-1).
%C Odd bisection of A305422 and A305425.
%H Antti Karttunen, <a href="/A305424/b305424.txt">Table of n, a(n) for n = 1..8191</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) = A305422(2*n-1).
%o (PARI)
%o A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
%o A305419(n) = if(n<3,1, my(k=n-1); while(k>1 && !A091225(k),k--); (k));
%o A305422(n) = { my(f = subst(lift(factor(Pol(binary(n))*Mod(1, 2))),x,2)); for(i=1,#f~,f[i,1] = Pol(binary(A305419(f[i,1])))); fromdigits(Vec(factorback(f))%2,2); };
%o A305424(n) = A305422(n+n-1);
%Y Cf. A305423 (inverse).
%Y Cf. A014580, A091225, A304522, A305425.
%Y Cf. also A064216.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jun 08 2018