cp's OEIS Frontend

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.

%I A298519 #6 Jan 10 2024 16:10:52
%S A298519 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,
%T A298519 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,
%U A298519 2,3,8,5,0,9,2,3,4,3,7,3,1,5,9,0,5,3
%N 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.
%C A298519 (lim_ {n->oo} s(n)) = g = real zero of x^3 - x - 1.  See A298512 for a guide to related sequences.
%e A298519 s(0) + s(1) + ... + s(n) - (n+1)*g -> 0.819904707664104372564776035917499198052...
%t A298519 s[0] = 2; d = 1; p = 1/3;
%t A298519 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[3]]
%t A298519 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298519 N[Table[s[n], {n, 0, 30}]]
%t A298519 s = N[Sum[-g + s[n], {n, 0, 200}], 150 ];
%t A298519 RealDigits[s, 10][[1]] (* A298519 *)
%Y A298519 Cf. A298512, A298518, A298520.
%K A298519 nonn,easy,cons
%O A298519 0,1
%A A298519 _Clark Kimberling_, Feb 11 2018