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 A100341 #5 Mar 30 2012 18:36:44 %S A100341 1,2,3,14,17,48,65,568,633,1834,2467,11702,14169,40040,54209,907384, %T A100341 961593,2830570,3792163,17999222,21791385,61581992,83373377,728569008, %U A100341 811942385,2352453778,3164396163,15010038430,18174434593,51358907616 %N A100341 Denominators of the convergents in the continued fraction expansion for the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n). %C A100341 The convergents for the continued fraction of x are given by A100340(n)/A100341(n) and the convergents for the continued fraction of 2*x are given by A100342(n)/A100343(n), where A100342(n)/A100343(n) = 2*A100340(n)/A100341(n) for all n. %F A100341 a(1) = 1, a(2) = 2, a(n) = a(n-1)*A006519(n) + a(n-2). %e A100341 The constant is x=1.353871128429882374388894084016608124227333416812... %e A100341 contfrac(x) = [1;2,1,4,1,2,1,8,1,2,1,4,1,2,1,16,...A006519(n),... ]. %o A100341 (PARI) a(n)=if(n==1,1,if(n==2,2,a(n-1)*2^valuation(n,2)+a(n-2))) %Y A100341 Cf. A100338, A006519, A100340, A100342, A100343. %K A100341 cofr,nonn %O A100341 1,2 %A A100341 _Paul D. Hanna_, Nov 18 2004