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A296222 Decimal expansion of the limiting ratio of terms in A296221.

%I A296222 #12 Mar 15 2025 05:47:31
%S A296222 3,6,5,1,1,1,9,4,2,2,2,3,8,0,3,4,7,5,8,6,4,0,5,0,0,5,1,9,7,9,2,7,3,1,
%T A296222 3,8,8,9,8,5,2,8,9,7,5,8,3,6,3,3,5,4,0,1,5,3,1,6,7,9,4,8,7,3,9,5,9,6,
%U A296222 9,0,3,2,6,0,2,0,8,4,2,4,0,5,4,2,8,9
%N A296222 Decimal expansion of the limiting ratio of terms in A296221.
%C A296222 See A296000 for a guide to related sequences and limiting ratios.
%e A296222 A296221(n)/A296221(n-1) -> 3.651119422238034...
%t A296222 mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];
%t A296222 a[0] = 1; a[1] = 3; b[0] = 2;
%t A296222 a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 0, n - 1}] + 1;
%t A296222 b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
%t A296222 u = Table[a[n], {n, 0, 200}];  (* A296221 *)
%t A296222 Table[b[n], {n, 0, 20}]
%t A296222 N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
%t A296222 RealDigits[Last[t], 10][[1]] (* A296222 *)
%Y A296222 Cf. A296000, A296221.
%K A296222 nonn,easy,cons
%O A296222 1,1
%A A296222 _Clark Kimberling_, Dec 09 2017