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 A245225 #9 Jul 07 2024 10:16:29
%S A245225 2,1,2,2,2,1,2,2,2,1,2,2,1,2,2,2,1,2,2,1,2,2,2,1,2,2,1,2,2,2,1,2,2,1,
%T A245225 2,2,2,1,2,2,2,1,2,2,1,2,2,2,1,2,2,1,2,2,2,1,2,2,1,2,2,2,1,2,2,1,2,2,
%U A245225 2,1,2,2,1,2,2,2,1,2,2,2,1,2,2,1,2,2
%N A245225 Continued fraction expansion of the constant c in A245224; c = sup{f(n,1)}, where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A054385, else f(n,x) = 1/x.
%C A245225 See Comments at A245215.
%e A245225 c = 2.70777871600507812434020666596313162... ; The first 16 numbers f(n,1) comprise S(16) = {1, 2, 1/2, 3/2, 5/2, 2/5, 7/5, 12/5, 5/12, 17/12, 12/17, 29/17}; max(S(16)) = 46/17, with continued fraction [2, 1, 2, 2, 2].
%t A245225 tmpRec = $RecursionLimit; $RecursionLimit = Infinity; u[x_] := u[x] = x + 1; d[x_] := d[x] = 1/x; r = E/(E-1); w = Table[Floor[k*r], {k, 2000}]; s[1] = 1; s[n_] := s[n] = If[MemberQ[w, n - 1], u[s[n - 1]], d[s[n - 1]]]; max = Max[N[Table[s[n], {n, 1, 3000}], 200]] (* A245224 *)
%t A245225 ContinuedFraction[max, 120] (* A245225 *)
%Y A245225 Cf. A226080 (infinite Fibonacci tree), A245217, A245219, A245222, A245224 (decimal expansion).
%K A245225 nonn,cofr,easy
%O A245225 0,1
%A A245225 _Clark Kimberling_, Jul 14 2014
%E A245225 Offset changed by _Andrew Howroyd_, Jul 07 2024