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A304529 a(1) = 0, a(2n) = n, a(2n+1) = a(A305422(2n+1)).

%I A304529 #8 Jun 10 2018 21:14:19
%S A304529 0,1,1,2,2,3,1,4,3,5,1,6,1,7,4,8,8,9,1,10,2,11,11,12,1,13,6,14,7,15,1,
%T A304529 16,25,17,7,18,1,19,14,20,1,21,19,22,12,23,1,24,3,25,16,26,13,27,1,28,
%U A304529 22,29,1,30,1,31,5,32,10,33,1,34,2,35,59,36,1,37,44,38,55,39,13,40,2,41,9,42,32,43,1,44,47,45,1,46,19,47,26,48,1,49,50,50
%N A304529 a(1) = 0, a(2n) = n, a(2n+1) = a(A305422(2n+1)).
%C A304529 This is GF(2)[X] analog of A246277.
%C A304529 For all i, j: a(i) = a(j) => A278233(i) = A278233(j).
%C A304529 For all i, j: a(i) = a(j) => A305788(i) = A305788(j).
%H A304529 Antti Karttunen, <a href="/A304529/b304529.txt">Table of n, a(n) for n = 1..65537</a>
%H A304529 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%F A304529 a(1) = 0, a(2n) = n, a(2n+1) = a(A305422(2n+1)).
%o A304529 (PARI)
%o A304529 A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
%o A304529 A305419(n) = if(n<3,1, my(k=n-1); while(k>1 && !A091225(k),k--); (k));
%o A304529 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 A304529 A304529(n) = if(1==n,0,while(n%2, n = A305422(n)); n/2);
%Y A304529 Cf. A305422, A305425.
%Y A304529 Cf. A014580 (positions of 1's), A278233, A305788.
%Y A304529 Cf. also A246277.
%K A304529 nonn
%O A304529 1,4
%A A304529 _Antti Karttunen_, Jun 10 2018