cp's OEIS Frontend

A298518 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = 1.324717957..., s(n) = (s(n - 1) + 1)^(1/3), s(0) = 1.

%I A298518 #6 Jan 10 2024 16:10:37
%S A298518 4,0,4,8,5,7,6,7,7,4,2,6,2,4,9,6,1,3,2,6,2,9,0,6,0,7,4,4,5,8,0,2,0,3,
%T A298518 0,0,1,4,6,6,8,6,8,2,3,9,6,9,5,7,4,7,9,9,4,3,5,8,7,9,3,8,2,3,8,4,6,2,
%U A298518 9,7,5,1,8,8,8,5,4,5,7,8,8,5,8,9,4,9
%N A298518 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = 1.324717957..., s(n) = (s(n - 1) + 1)^(1/3), s(0) = 1.
%C A298518 (lim_ {n->oo} s(n)) = g = real zero of x^3 - x - 1.  See A298512 for a guide to related sequences.
%e A298518 ((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 0.40485767742624961326290607445802...
%t A298518 s[0] = 1; d = 1; p = 1/3;
%t A298518 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[3]]
%t A298518 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298518 N[Table[s[n], {n, 0, 30}]]
%t A298518 s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
%t A298518 RealDigits[s, 10][[1]] (* A298518 *)
%Y A298518 Cf. A298512, A298519, A298520.
%K A298518 nonn,easy,cons
%O A298518 0,1
%A A298518 _Clark Kimberling_, Feb 11 2018