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 A072729 #4 Mar 30 2012 18:36:32 %S A072729 1,1,2,2,3,3,5,5,5,5,8,7,8,8,7,8,12,13,11,12,13,12,13,11,12,13,19,19, %T A072729 21,17,18,19,19,21,19,19,21,17,18,19,19,21,29,31,30,31,34,27,26,29,29, %U A072729 31,30,31,34 %N A072729 Denominator of rationals >= 1 whose continued fractions consist only of 1's and 2's, in ascending order by the sum of the continued fraction terms and descending by lowest order continued fraction terms to highest. %F A072729 a(F(n)+F(n-3)+m) = a(F(n-1)+m) + a(F(n-3)+m) when 0<m<=F(n-2), n>2; a(F(n)+m) = 2*a(F(n-2)+m) + a(F(n-4)+m) when 0<m<=F(n-3), n>3; where a(0)=1, a(F(n+1)-1) = F(n) = n-th Fibonacci number; a(F(2n+1)) = n-th Pell number. %Y A072729 Cf. A072728, A071585, A071766, A072726, A072727, A000129. %K A072729 easy,frac,nice,nonn %O A072729 0,3 %A A072729 _Paul D. Hanna_, Jul 09 2002