cp's OEIS Frontend

A298523 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n + 1)*g), where g = 1.86676039917386..., s(n) = (s(n - 1) + (1+sqrt(5))/2)^(1/2), s(0) = 2.

%I A298523 #6 Jan 10 2024 16:13:04
%S A298523 1,8,1,4,9,0,0,8,3,3,3,4,2,5,0,7,8,0,8,2,2,5,3,9,3,1,2,6,3,7,4,2,1,9,
%T A298523 8,4,3,5,7,7,0,3,6,3,4,3,7,5,9,7,0,3,7,2,4,9,9,5,1,2,3,0,6,2,4,0,8,4,
%U A298523 1,8,3,7,8,5,4,4,3,7,2,2,5,5,6,6,6,2
%N A298523 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n + 1)*g), where g = 1.86676039917386..., s(n) = (s(n - 1) + (1+sqrt(5))/2)^(1/2), s(0) = 2.
%C A298523 (lim_ {n->oo} s(n)) = g = real zero of x^2 - x - (1+sqrt(5))/2.  See A298512 for a guide to related sequences.
%e A298523 s(0) + s(1) + ... + s(n) - (n + 1)*g -> 0.1814900833342507808225393126374219...
%t A298523 s[0] = 2; d = GoldenRatio; p = 1/2;
%t A298523 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
%t A298523 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298523 N[Table[s[n], {n, 0, 30}]]
%t A298523 s = N[Sum[- g + s[n], {n, 0, 200}], 150 ];
%t A298523 RealDigits[s, 10][[1]] (* A298523 *)
%Y A298523 Cf. A298512, A298522.
%K A298523 nonn,easy,cons
%O A298523 0,2
%A A298523 _Clark Kimberling_, Feb 12 2018