This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305424 #6 Jun 08 2018 13:52:57 %S A305424 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 A305424 26,47,44,55,59,10,20,61,21,118,67,88,110,53,69,18,64,73,94,87,43,52, %U A305424 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 A305424 Permutation of natural numbers: a(n) = A305422(2*n-1). %C A305424 Odd bisection of A305422 and A305425. %H A305424 Antti Karttunen, <a href="/A305424/b305424.txt">Table of n, a(n) for n = 1..8191</a> %H A305424 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a> %H A305424 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %F A305424 a(n) = A305422(2*n-1). %o A305424 (PARI) %o A305424 A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2)); %o A305424 A305419(n) = if(n<3,1, my(k=n-1); while(k>1 && !A091225(k),k--); (k)); %o A305424 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 A305424(n) = A305422(n+n-1); %Y A305424 Cf. A305423 (inverse). %Y A305424 Cf. A014580, A091225, A304522, A305425. %Y A305424 Cf. also A064216. %K A305424 nonn %O A305424 1,2 %A A305424 _Antti Karttunen_, Jun 08 2018