A295999 Decimal expansion of the limiting ratio of terms in A296000.

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

Offset

1,1

Comments

A296000(n)/A296000(n-1)) -> 3.65118837444960841368821041192011...

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

Links

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

Mathematica

$RecursionLimit = Infinity;
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}];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
Table[a[n], {n, 0, 100}]  (* A296000 *)
t = N[Table[a[n]/a[n - 1], {n, 1, 500, 100}], 200]
Take[RealDigits[Last[t], 10][[1]], 100]  (* A295999 *)

Crossrefs

Cf. A296000.

Sequence in context: A367036 A296226 A296222 * A296224 A135097 A154008

Adjacent sequences: A295996 A295997 A295998 * A296000 A296001 A296002

Keyword

nonn,easy,cons

Author

Clark Kimberling, Dec 04 2017

Status

approved