A296004 Decimal expansion of the limiting ratio of terms in A296003.

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

Offset

1,1

Comments

A296003(n)/A296003(n-1)) -> 2.961844324.....

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] = 2; a[1] = 4; 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}];  (* A296003 *)
t = N[Table[a[n]/a[n - 1], {n, 1, 500, 100}], 200]
Take[RealDigits[Last[t], 10][[1]], 100]  (* A296004 *)

Crossrefs

Cf. A296000, A296003.

Sequence in context: A162916 A057273 A236558 * A108986 A011069 A010598

Adjacent sequences: A296001 A296002 A296003 * A296005 A296006 A296007

Keyword

nonn,easy,cons

Author

Clark Kimberling, Dec 07 2017

Status

approved