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%I #6 Jan 10 2024 16:14:01
%S 1,2,5,5,1,3,0,8,0,8,1,4,4,2,5,3,9,2,4,3,3,5,1,8,6,4,0,4,6,3,5,8,1,6,
%T 9,5,7,6,7,6,5,1,2,6,0,3,6,8,1,5,5,7,8,3,1,2,6,0,5,4,8,7,7,9,8,0,4,6,
%U 8,3,8,2,9,1,5,7,3,6,5,3,3,9,6,8,7,2
%N Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.9078532620869538..., s(n) = (s(n - 1) + sqrt(3))^(1/2), s(0) = 1.
%C (lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - sqrt(3). See A298512 for a guide to related sequences.
%e (n+1)*g - s(0) - s(1) - ... - s(n) -> 1.255130808144253924335186404635816957676...
%t s[0] = 1; d = Sqrt[3]; 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]] (* A298526 *)
%Y Cf. A298512, A298527.
%K nonn,easy,cons
%O 1,2
%A _Clark Kimberling_, Feb 12 2018
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