A296002 Decimal expansion of the limiting ratio of terms in A296001.

4, 3, 0, 2, 8, 0, 9, 1, 8, 3, 9, 1, 8, 5, 8, 8, 7, 3, 1, 1, 7, 8, 6, 3, 0, 0, 9, 8, 8, 2, 5, 5, 0, 4, 8, 3, 4, 9, 9, 1, 5, 4, 5, 9, 8, 6, 7, 0, 6, 2, 7, 0, 7, 7, 8, 0, 0, 1, 4, 3, 9, 9, 1, 2, 7, 7, 0, 4, 8, 2, 2, 7, 5, 9, 8, 8, 0, 0, 6, 0, 8, 8, 2, 6, 0, 8

Offset: 1

Author

Clark Kimberling, Dec 04 2017

Keywords

• nonn
• easy
• cons

Comments

A296001(n)/A296001(n-1) -> 4.302809183918588...

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

Crossrefs

Cf. A296000, A296001.

Programs

Mathematica

mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];
a[0] = 1; a[1] = 2; b[0] = 3;
a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 0, n - 1}];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
Table[a[n], {n, 0, 100}];  (* A296001 *)
t = N[Table[a[n]/a[n - 1], {n, 1, 500, 100}], 200]
Take[RealDigits[Last[t], 10][[1]], 100]  (* A296002 *)