A298521 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = 2.1478990357..., s(n) = (s(n - 1) + 1)^(2/3), s(0) = 1.

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

Offset

1,1

Comments

(lim_ {n->oo} s(n)) = g = real zero of x^(2/3) - x - 1. See A298512 for a guide to related sequences.

Links

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

Example

((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 2.19524431421173816419739210020867...

Mathematica

s[0] = 1; d = 1; p = 2/3;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])
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]] (* A298521 *)

Crossrefs

Cf. A298512, A298520.

Sequence in context: A293417 A295737 A021086 * A177972 A011136 A361146

Adjacent sequences: A298518 A298519 A298520 * A298522 A298523 A298524

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 12 2018

Status

approved