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

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..86.

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 *)

Crossrefs

Cf. A296000, A296001.

Sequence in context: A284056 A338149 A338145 * A227423 A199443 A142723

Adjacent sequences: A295999 A296000 A296001 * A296003 A296004 A296005

Keyword

nonn,easy,cons

Author

Clark Kimberling, Dec 04 2017

Status

approved