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 A179823 #7 Nov 03 2016 05:28:01 %S A179823 1,1,2,5,29,408,33461,38613965,3654502875938,399133058537705128729, %T A179823 4125636888562548868221559797461449, %U A179823 4657508918199804645965719872781284840798220312648198320 %N A179823 Denominators in the approximation of sqrt(2) satisfying the recurrence: a(n)= [a(n-1)*a(n-2)+2]/[a(n-1)+a(n-2)] with a(1)=a(2)=1. %C A179823 The recurrence is a transform of the Babylonian (Newton's) method for square root computation: a(n+1)= N/2a(n)+a(n)/2 = (a(n)^2+N)/2a(n). %e A179823 1/1=1.0, 1/1=1.0, 3/2=1.5, 7/5=1.4, 42/29=1.41379.., 577/408=1.4142156,... - _R. J. Mathar_, Nov 03 2016 %t A179823 a[1] = a[2] = 1; a[n_] := (a[n - 1] a[n - 2] + 2)/(a[n - 1] + a[n - 2]); Denominator@ Array[ a, 12] (* _Robert G. Wilson v_, Aug 03 2010 *) %Y A179823 Cf. A179907, A000129, A051009. %K A179823 nonn,frac %O A179823 1,3 %A A179823 _Mark Dols_, Jul 28 2010 %E A179823 a(10) - a(12) from _Robert G. Wilson v_, Aug 03 2010