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 A215976 #8 Aug 30 2012 12:05:06 %S A215976 1,0,2,2,0,2,3,3,3,3,2,0,3,0,4,4,4,4,4,4,4,4,3,3,0,3,4,4,0,4,5,5,5,5, %T A215976 5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,3,2,4,0,5,5,5,5,4,0,5,0,6,6,6,6,6,6, %U A215976 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6 %N A215976 2-adic valuation of the denominator of sum( k!/2^k, k=1..n ). %C A215976 By construction, this denominator is always a power of 2, the present sequence specifies which power. The sum is an integer iff a(n)=0, the corresponding n are listed in A215974 (= A215972 - 1). %F A215976 denominator( sum( k!/2^k, k=1..n )) = 2^a(n). %F A215976 a(n)=0 <=> n is in A215974 <=> n+1 is in A215972. %o A215976 (PARI) s=0;for(k=1,199,print1(valuation(denominator(s+=k!/2^k),2),",")) %Y A215976 The numerator of the sum is given in A215990. %K A215976 nonn %O A215976 1,3 %A A215976 _M. F. Hasler_, Aug 29 2012