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 A100340 #9 May 15 2014 09:51:21 %S A100340 1,3,4,19,23,65,88,769,857,2483,3340,15843,19183,54209,73392,1228481, %T A100340 1301873,3832227,5134100,24368627,29502727,83374081,112876808, %U A100340 986388545,1099265353,3184919251,4284184604,20321657667,24605842271,69533342209 %N A100340 Numerators 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 A100340 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 A100340 a(1) = 1, a(2) = 3, a(n) = a(n-1)*A006519(n) + a(n-2). %e A100340 The constant is x=1.353871128429882374388894084016608124227333416812... %e A100340 contfrac(x) = [1;2,1,4,1,2,1,8,1,2,1,4,1,2,1,16,...A006519(n),... ]. %t A100340 Convergents[ Array[ 2^IntegerExponent[#, 2]&, 30] ] // Numerator (* _Jean-François Alcover_, May 15 2014 *) %o A100340 (PARI) a(n)=if(n==1,1,if(n==2,3,a(n-1)*2^valuation(n,2)+a(n-2))) %Y A100340 Cf. A100338, A006519, A100341, A100342, A100343. %K A100340 cofr,nonn %O A100340 1,2 %A A100340 _Paul D. Hanna_, Nov 18 2004