cp's OEIS Frontend

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.

%I A298520 #6 Jan 10 2024 16:11:25
%S A298520 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,
%T A298520 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,
%U A298520 7,0,8,3,8,6,2,9,6,4,8,8,2,5,2,4,6,9
%N 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.
%C A298520 (lim_ {n->oo} s(n)) = g = real zero of x^3 - x - 1.  See A298512 for a guide to related sequences.
%e A298520 s(0) + s(1) + ... + s(n) - (n+1)*g -> 1.9972964760109796754339092295853245...
%t A298520 s[0] = 3; d = 1; p = 1/3;
%t A298520 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[3]]
%t A298520 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298520 N[Table[s[n], {n, 0, 30}]]
%t A298520 s = N[Sum[- g + s[n], {n, 0, 200}], 150 ];
%t A298520 RealDigits[s, 10][[1]] (* A298520 *)
%Y A298520 Cf. A298512, A298518, A298519.
%K A298520 nonn,easy,cons
%O A298520 1,2
%A A298520 _Clark Kimberling_, Feb 11 2018