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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
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A028602 A111767 A111511 * A021251 A160207 A190103

Adjacent sequences:  A298515 A298516 A298517 * A298519 A298520 A298521

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Feb 11 2018

STATUS

approved

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Last modified February 17 11:58 EST 2020. Contains 331996 sequences. (Running on oeis4.)