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%I #6 Jan 10 2024 16:07:51
%S 5,9,0,7,3,1,6,8,1,5,1,8,0,7,7,5,7,4,1,8,5,9,7,9,5,1,7,6,8,4,1,9,4,7,
%T 8,7,9,3,0,3,2,4,0,0,1,2,4,1,6,7,7,9,9,7,1,2,9,7,8,1,6,3,6,7,0,4,9,8,
%U 3,9,7,7,8,6,4,2,9,8,2,4,5,8,0,0,1,7
%N Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) -s(1) - ... - s(n)), where g = (1 + sqrt (3))/2, s(n) = (s(n - 1) + 1/2)^(1/2), s(0) = 1.
%C (lim_ {n->oo} s(n)) = g = (1 + sqrt (3))/2. See A298512 for a guide to related sequences.
%e s(n) -> g = (1+sqrt(3))/2.
%e (n+1)*g - s(0) - s(1) - ... - s(n) -> 0.590731681518077574185979517684194787...
%t s[0] = 1; d = 1/2; 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 StringJoin[StringTake[ToString[s], 41], "..."]
%t RealDigits[s, 10][[1]] (* A298515 *)
%Y Cf. A298512, A298516, A298517.
%K nonn,easy,cons
%O 0,1
%A _Clark Kimberling_, Feb 11 2018
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