A298520 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 1.324717957..., s(n) = (s(n - 1) + 1)^(1/3), s(0) = 3.

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

Offset

1,2

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=1..86.

Example

s(0) + s(1) + ... + s(n) - (n+1)*g -> 1.9972964760109796754339092295853245...

Mathematica

s[0] = 3; 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]] (* A298520 *)

Crossrefs

Cf. A298512, A298518, A298519.

Sequence in context: A072908 A217695 A197390 * A270712 A277587 A372828

Adjacent sequences: A298517 A298518 A298519 * A298521 A298522 A298523

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 11 2018

Status

approved