cp's OEIS Frontend

A296228 Decimal expansion of the limiting ratio of terms in A296227.

%I A296228 #11 Mar 15 2025 06:30:33
%S A296228 4,3,0,3,3,9,6,3,0,3,1,3,3,0,4,0,0,6,6,1,7,5,7,5,8,0,9,6,3,3,2,1,4,8,
%T A296228 7,1,3,8,8,6,4,4,1,0,2,0,2,7,2,6,5,2,3,4,1,5,1,6,0,7,0,7,8,7,6,6,8,3,
%U A296228 5,8,2,3,1,4,6,6,8,7,0,5,0,2,3,8,2,4
%N A296228 Decimal expansion of the limiting ratio of terms in A296227.
%C A296228 See A296000 for a guide to related sequences and limiting ratios.
%F A296228 Equals lim_{n->oo} A296227(n)/A296227(n-1).
%e A296228 4.3033963031...
%t A296228 mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];
%t A296228 a[0] = 1; a[1] = 2; b[0] = 3;
%t A296228 a[n_] := a[n] = - n + Sum[a[k]*b[n - k - 1], {k, 0, n - 1}];
%t A296228 b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
%t A296228 Table[a[n], {n, 0, 200}]  (* A296227 *)
%t A296228 Table[b[n], {n, 0, 20}]
%t A296228 N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
%t A296228 RealDigits[Last[t], 10][[1]] (* A296228 *)
%Y A296228 Cf. A296000, A296227.
%K A296228 nonn,easy,cons
%O A296228 1,1
%A A296228 _Clark Kimberling_, Dec 10 2017