cp's OEIS Frontend

A298522 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = 1.86676039917386..., s(n) = (s(n - 1) + (1+sqrt(5))/2)^(1/2), s(0) = 1.

%I A298522 #6 Jan 10 2024 16:12:17
%S A298522 1,2,0,8,2,9,3,7,9,7,2,2,6,7,6,7,8,2,5,1,8,5,9,1,5,4,9,9,5,6,0,9,5,2,
%T A298522 7,8,9,5,9,0,1,9,6,8,9,6,0,8,0,9,8,8,5,5,6,7,8,7,0,0,7,2,7,8,1,5,2,0,
%U A298522 1,2,7,4,3,3,5,5,2,2,1,3,7,9,1,0,3,7
%N A298522 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = 1.86676039917386..., s(n) = (s(n - 1) + (1+sqrt(5))/2)^(1/2), s(0) = 1.
%C A298522 (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 A298522 ((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 1.20829379722676782518591549956095278...
%t A298522 s[0] = 1; d = GoldenRatio; p = 1/2;
%t A298522 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
%t A298522 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298522 N[Table[s[n], {n, 0, 30}]]
%t A298522 s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
%t A298522 RealDigits[s, 10][[1]] (* A298522 *)
%Y A298522 Cf. A298512, A298523.
%K A298522 nonn,easy,cons
%O A298522 1,2
%A A298522 _Clark Kimberling_, Feb 12 2018