cp's OEIS Frontend

A298516 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.

%I A298516 #6 Jan 10 2024 16:08:16
%S A298516 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 A298516 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 A298516 6,9,1,5,7,2,8,2,3,5,6,2,9,4,1,5,7,4
%N A298516 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 A298516 See A298512 for a guide to related sequences.
%e A298516 2n + 2 - s(0) - s(1) - ... - s(n) -> 1.358917762842788340395837672187105945234...
%t A298516 s[0] = 1; d = 2; p = 1/2;
%t A298516 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
%t A298516 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298516 N[Table[s[n], {n, 0, 30}]];
%t A298516 s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
%t A298516 StringJoin[StringTake[ToString[s], 41], "..."]
%t A298516 u = RealDigits[s, 10][[1]]   (* A298516 *)
%Y A298516 Cf. A298512, A298516, A298517.
%K A298516 nonn,easy,cons
%O A298516 1,2
%A A298516 _Clark Kimberling_, Feb 11 2018