%I #6 Jan 10 2024 16:16:31
%S 3,4,1,5,3,3,3,9,8,0,5,2,9,0,5,7,3,2,1,9,5,0,4,3,4,3,7,0,6,6,2,3,3,3,
%T 0,6,0,7,7,0,1,2,2,2,7,4,7,1,1,6,1,5,0,3,8,9,0,1,9,9,5,2,7,0,5,0,4,8,
%U 6,6,6,5,4,5,1,9,1,9,1,7,3,0,0,2,4,5
%N Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.866760399173862092990..., s(n) = (s(n - 1) + tau)^(1/2), s(0) = tau = (1+sqrt(5))/2 (golden ratio).
%C (lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - tau. See A298512 for a guide to related sequences.
%e lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)) -> 0.3415333980529057321950...
%t tau = GoldenRatio;
%t s[0] = tau; d = tau; p = 1/2;
%t g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
%t s[n_] := s[n] = (s[n - 1] + d)^p
%t N[Table[s[n], {n, 0, 30}]]
%t s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
%t RealDigits[s, 10][[1]] (* A298532 *)
%Y Cf. A298512, A298531.
%K nonn,easy,cons
%O 0,1
%A _Clark Kimberling_, Feb 13 2018