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

Author

Clark Kimberling, Dec 07 2017

Keywords

• nonn
• easy
• cons

Comments

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

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

Crossrefs

Cf. A296000, A296003.

Programs

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 *)