cp's OEIS Frontend

A277013 a(n) = number of irreducible polynomial factors (counted with multiplicity) in the n-th Stern polynomial B(n,t).

%I A277013 #17 Oct 09 2016 19:42:36
%S A277013 0,1,1,2,1,2,1,3,2,2,1,3,1,2,2,4,1,3,1,3,2,2,1,4,1,2,3,3,1,3,1,5,2,2,
%T A277013 2,4,1,2,2,4,1,3,1,3,3,2,1,5,2,2,2,3,1,4,1,4,2,2,1,4,1,2,3,6,1,3,1,3,
%U A277013 2,3,1,5,1,2,3,3,1,3,1,5,2,2,1,4,2,2,2,4,1,4,1,3,2,2,1,6,1,3,3,3,1,3,1,4,3,2,1,5,1,2,2,5,1,3,1,3,2,2,2,5
%N A277013 a(n) = number of irreducible polynomial factors (counted with multiplicity) in the n-th Stern polynomial B(n,t).
%H A277013 Antti Karttunen, <a href="/A277013/b277013.txt">Table of n, a(n) for n = 1..85085</a>
%F A277013 a(n) = A277322(A260443(n)).
%F A277013 It seems that for all n >= 1, a(2^n) = n.
%e A277013 B(11,t) = t^2 + 3t + 1 which is irreducible, so a(11) = 1.
%e A277013 B(12,t) = t^3 + t^2 = t^2(t+1), so a(12) = 3.
%o A277013 (PARI)
%o A277013 A277013 = n -> vecsum(factor(ps(n))[,2]);
%o A277013 ps(n) = if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2))); \\ From _Charles R Greathouse IV_ code in A186891.
%o A277013 for(n=1, 85085, write("b277013.txt", n, " ", A277013(n)));
%Y A277013 Cf. A186891 (positions of 0 and 1's in this sequence), A277027 (terms squared).
%Y A277013 Cf. A000079, A125184, A277322, A260443.
%Y A277013 Differs from A001222 for the first time at n=25, where a(25)=1. A277190 gives the positions of differing terms.
%K A277013 nonn
%O A277013 1,4
%A A277013 _Antti Karttunen_, Oct 07 2016