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A298519
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) = 2.
4
8, 1, 9, 9, 0, 4, 7, 0, 7, 6, 6, 4, 1, 0, 4, 3, 7, 2, 5, 6, 4, 7, 7, 6, 0, 3, 5, 9, 1, 7, 4, 9, 9, 1, 9, 8, 0, 5, 2, 9, 0, 6, 1, 3, 1, 9, 6, 1, 2, 5, 0, 4, 9, 2, 5, 1, 4, 9, 4, 1, 3, 4, 4, 9, 0, 5, 9, 2, 2, 3, 8, 5, 0, 9, 2, 3, 4, 3, 7, 3, 1, 5, 9, 0, 5, 3
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.
EXAMPLE
s(0) + s(1) + ... + s(n) - (n+1)*g -> 0.819904707664104372564776035917499198052...
MATHEMATICA
s[0] = 2; 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]] (* A298519 *)
CROSSREFS
KEYWORD
nonn,easy,cons
AUTHOR
Clark Kimberling, Feb 11 2018
STATUS
approved