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 A114912 #11 Aug 24 2024 06:03:23 %S A114912 0,0,0,1,1,0,2,0,1,3,1,2,0,1,1,0,5,1,1,1,6,2,0,3,1,1,0,6,1,8,3,2,1,6, %T A114912 9,0,2,3,5,1,0,2,1,1,3,11,8,1,1,6,1,0,1,10,1,1,2,0,3,6,7,2,1,9,2,3,2, %U A114912 1,13,1,0,5,9,1,1,1,1,0,1,3,9,2,6,1,1,6,6,1,1,1,1,11,0,5,6,1,2,8,6,1,0,1 %N A114912 2^a(n) divides A000009(n) but 2^(a(n)+1) does not. %C A114912 Almost all members of A000009 are divisible by 2^k for any k, therefore almost all a(n)>k for any k. %H A114912 Amiram Eldar, <a href="/A114912/b114912.txt">Table of n, a(n) for n = 0..10000</a> %H A114912 Krishnaswami Alladi, <a href="https://doi.org/10.1090/S0002-9947-97-01831-X">Partition Identities Involving Gaps and Weights</a>, Transactions of the American Mathematical Society, Vol. 349, No. 12 (Dec 1997), pp. 5001-5019. %H A114912 Basil Gordon and Ken Ono, <a href="https://doi.org/10.1023/A:1009711020492">Divisibility of certain partition functions by powers of primes</a>, The Ramanujan Journal, Vol. 1, No. 1 (1997), pp. 25-34; <a href="https://uva.theopenscholar.com/files/ken-ono/files/018.pdf">alternative link</a>. %F A114912 a(n) = A007814(A000009(n)). - _Max Alekseyev_, Apr 27 2010 %t A114912 a[n_] := IntegerExponent[PartitionsQ[n], 2]; Array[a, 100, 0] (* _Amiram Eldar_, Aug 24 2024 *) %Y A114912 Cf. A000009, A007814. %Y A114912 Cf. A001318 (positions of 0's), A114913 (positions of 1's), A115251 (least inverse). %K A114912 nonn %O A114912 0,7 %A A114912 _Christian G. Bower_, Jan 06 2006