cp's OEIS Frontend

A278478 a(n) is the 2-adic valuation of A000041(n).

%I A278478 #20 Nov 19 2024 23:46:37
%S A278478 0,0,1,0,0,0,0,0,1,1,1,3,0,0,0,4,0,0,0,1,0,3,1,0,0,1,2,1,1,0,2,1,0,0,
%T A278478 1,0,0,0,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,2,0,1,2,2,0,0,2,0,1,1,6,0,
%U A278478 0,0,5,0,0,0,2,3,0,0,2,1,2,0,0,0,2,0,1,0,0,0,0,0,0,0,3,0,11,1,3,0,2,1,0,1,0,0,4,0,2,7,1,0,2,2,0,0,3,2,0
%N A278478 a(n) is the 2-adic valuation of A000041(n).
%C A278478 Write A000041(n) = 2^k * s where s is odd, then a(n) = k.
%H A278478 Joerg Arndt, <a href="/A278478/b278478.txt">Table of n, a(n) for n = 0..10000</a>
%F A278478 From _Amiram Eldar_, May 25 2024: (Start)
%F A278478 a(n) = A007814(A000041(n)).
%F A278478 a(n) = log_2(A069935(n)). (End)
%p A278478 a:= n-> padic[ordp](combinat[numbpart](n), 2):
%p A278478 seq(a(n), n=0..120);  # _Alois P. Heinz_, Nov 23 2016
%t A278478 a[n_] := IntegerExponent[PartitionsP[n], 2]; Array[a, 100, 0] (* _Amiram Eldar_, May 25 2024 *)
%o A278478 (PARI) { my( x='x+O('x^100), v=Vec(1/eta(x)) ); vector(#v,n,valuation(v[n],2)) }
%Y A278478 Cf. A000041, A007814, A069935, A278479.
%Y A278478 Cf. A052002, A237280, A278779, A278780, A278781, A278782, A278783, A278784 (positions of terms 0, 1, 2, ..., 7 in this sequence).
%Y A278478 Cf. also A278241.
%K A278478 nonn
%O A278478 0,12
%A A278478 _Joerg Arndt_, Nov 23 2016