cp's OEIS Frontend

A305425 a(n) = n/2 for even n, a(n) = A305422(n) for odd n.

%I A305425 #7 Jun 08 2018 13:53:04
%S A305425 1,1,2,2,4,3,3,4,6,5,7,6,11,7,8,8,16,9,13,10,5,11,22,12,19,13,12,14,
%T A305425 14,15,25,16,50,17,29,18,31,19,28,20,37,21,38,22,24,23,41,24,9,25,32,
%U A305425 26,26,27,47,28,44,29,55,30,59,31,10,32,20,33,61,34,21,35,118,36,67,37,88,38,110,39,53,40,69,41,18,42,64,43,73,44,94,45,87,46,43,47
%N A305425 a(n) = n/2 for even n, a(n) = A305422(n) for odd n.
%C A305425 Each k occurs exactly twice, at 2k and at A305421(k).
%H A305425 Antti Karttunen, <a href="/A305425/b305425.txt">Table of n, a(n) for n = 1..65537</a>
%H A305425 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%F A305425 a(n) = n/2 if n is even, a(n) = A305422(n) if n is odd.
%o A305425 (PARI)
%o A305425 A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
%o A305425 A305419(n) = if(n<3,1, my(k=n-1); while(k>1 && !A091225(k),k--); (k));
%o A305425 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 A305425 A305425(n) = if(n%2,A305422(n),n/2);
%Y A305425 Bisections: A000027 and A305422.
%Y A305425 Cf. also A252463.
%K A305425 nonn
%O A305425 1,3
%A A305425 _Antti Karttunen_, Jun 08 2018