cp's OEIS Frontend

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.

%I A298521 #6 Jan 10 2024 16:11:45
%S A298521 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,
%T A298521 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,
%U A298521 1,8,1,5,1,6,7,2,5,3,9,2,2,9,0,6,3,2
%N 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.
%C A298521 (lim_ {n->oo} s(n)) = g = real zero of x^(2/3) - x - 1.  See A298512 for a guide to related sequences.
%e A298521 ((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 2.19524431421173816419739210020867...
%t A298521 s[0] = 1; d = 1; p = 2/3;
%t A298521 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])
%t A298521 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298521 N[Table[s[n], {n, 0, 30}]]
%t A298521 s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
%t A298521 RealDigits[s, 10][[1]] (* A298521 *)
%Y A298521 Cf. A298512, A298520.
%K A298521 nonn,easy,cons
%O A298521 1,1
%A A298521 _Clark Kimberling_, Feb 12 2018