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

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, 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, 8, 2, 0, 0, 4, 6, 7, 1, 8, 8, 0, 6, 1, 5, 1, 3, 6, 5

Offset: 1

Author

Clark Kimberling, Dec 10 2017

Keywords

• nonn
• easy
• cons

Comments

See A296000 for a guide to related sequences and limiting ratios.

Examples

			3.651440004884...
		

Crossrefs

Cf. A296000, A296223.

Programs

Mathematica

mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];
a[0] = 1; a[1] = 3; b[0] = 2;
a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 0, n - 1}] - 1;
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
Table[a[n], {n, 0, 200}]  (* A296223 *)
Table[b[n], {n, 0, 20}]
N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
RealDigits[Last[t], 10][[1]] (* A296224 *)

Formula

Equals lim_{n->oo} A296223(n)/A296223(n-1).