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A296224 Decimal expansion of the limiting ratio of terms in A296223.

%I A296224 #11 Mar 15 2025 06:33:16
%S A296224 3,6,5,1,4,4,0,0,0,7,8,8,4,2,6,3,1,0,2,8,6,0,9,0,8,8,3,8,8,3,6,6,1,1,
%T A296224 5,6,6,2,1,0,9,9,1,7,9,0,0,6,0,5,3,2,3,8,8,7,1,7,8,0,2,9,0,3,3,0,3,1,
%U A296224 8,2,0,0,4,6,7,1,8,8,0,6,1,5,1,3,6,5
%N A296224 Decimal expansion of the limiting ratio of terms in A296223.
%C A296224 See A296000 for a guide to related sequences and limiting ratios.
%F A296224 Equals lim_{n->oo} A296223(n)/A296223(n-1).
%e A296224 3.651440004884...
%t A296224 mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];
%t A296224 a[0] = 1; a[1] = 3; b[0] = 2;
%t A296224 a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 0, n - 1}] - 1;
%t A296224 b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
%t A296224 Table[a[n], {n, 0, 200}]  (* A296223 *)
%t A296224 Table[b[n], {n, 0, 20}]
%t A296224 N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
%t A296224 RealDigits[Last[t], 10][[1]] (* A296224 *)
%Y A296224 Cf. A296000, A296223.
%K A296224 nonn,easy,cons
%O A296224 1,1
%A A296224 _Clark Kimberling_, Dec 10 2017