A296006 Decimal expansion of the limiting ratio of terms in A296005.

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

Offset: 1

Author

Clark Kimberling, Dec 07 2017

Keywords

• nonn
• easy
• cons

Comments

A296005(n)/A296005(n-1) -> 3.114986447390302...

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

Crossrefs

Cf. A296000, A296005.

Programs

Mathematica

mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];
a[0] = 2; a[1] = 3; b[0] = 1;
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}];  (* A296005 *)
t = N[Table[a[n]/a[n - 1], {n, 1, 500, 100}], 200]
Take[RealDigits[Last[t], 10][[1]], 100]  (* A296006 *)