A298521 - OEIS

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

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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])