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 A088458 #3 Mar 30 2012 18:36:39 %S A088458 1,2,4,6,7,8,13,11,12,18,22,20,27,27,24,32,35,34,39,43,44,42,44,53,56, %T A088458 54,60,67,69,59,72,75,76,72,83,81,87,81,96,99,102,107,108,106,105,112, %U A088458 114,115,121,130,125,129,125,131,135,152,149,139,139,150,154,161,162 %N A088458 a(n) equals the number of partial quotients of the simple continued fraction expansion of the nonsimple continued fraction: 1/(1+2/(2+3/(3+...+n/n)))). %C A088458 The finite nonsimple continued fraction, 1/(1+2/(2+3/(3+...+n/n)))), as n grows, has the limit: 1/(e-1) = [0;1,1,2,1,1,4,1,1,6,...] (A005131). %e A088458 a(5)=7 since there are 7 partial quotients in the resultant simple continued fraction of 1/(1+2/(2+3/(3+4/(4+5/5)))) = 53/91 = [0;1,1,2,1,1,7]. %e A088458 The count of partial quotients includes the initial integer position. %Y A088458 Cf. A005131. %K A088458 nonn %O A088458 1,2 %A A088458 _Paul D. Hanna_, Oct 01 2003