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%I #6 Jan 10 2024 16:08:16
%S 1,3,5,8,9,1,7,7,6,2,8,4,2,7,8,8,3,4,0,3,9,5,8,3,7,6,7,2,1,8,7,1,0,5,
%T 9,4,5,2,3,4,3,8,5,5,1,8,4,3,8,5,5,5,8,3,0,0,8,6,9,2,3,6,4,3,5,5,6,7,
%U 6,9,1,5,7,2,8,2,3,5,6,2,9,4,1,5,7,4
%N Decimal expansion of lim_ {n->oo} (2n+2 - s(0) - s(1) - ... - s(n)), where s(n) = (s(n - 1) + 2)^(1/2), s(0) = 1.
%C See A298512 for a guide to related sequences.
%e 2n + 2 - s(0) - s(1) - ... - s(n) -> 1.358917762842788340395837672187105945234...
%t s[0] = 1; d = 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 u = RealDigits[s, 10][[1]] (* A298516 *)
%Y Cf. A298512, A298516, A298517.
%K nonn,easy,cons
%O 1,2
%A _Clark Kimberling_, Feb 11 2018
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