A298518 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = 1.324717957..., s(n) = (s(n - 1) + 1)^(1/3), s(0) = 1.

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

Offset

0,1

Comments

(lim_ {n->oo} s(n)) = g = real zero of x^3 - x - 1. See A298512 for a guide to related sequences.

Links

Table of n, a(n) for n=0..85.

Example

((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 0.40485767742624961326290607445802...

Mathematica

s[0] = 1; d = 1; p = 1/3;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[3]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298518 *)

Crossrefs

Cf. A298512, A298519, A298520.

Sequence in context: A111767 A111511 A338828 * A021251 A160207 A190103

Adjacent sequences: A298515 A298516 A298517 * A298519 A298520 A298521

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 11 2018

Status

approved