cp's OEIS Frontend

A298524 Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.790044015672757..., s(n) = (s(n - 1) + sqrt(2))^(1/2), s(0) = 1.

%I A298524 #7 Jan 10 2024 16:13:25
%S A298524 1,1,1,9,7,9,1,8,0,7,3,0,4,6,0,8,2,9,6,5,4,6,4,8,8,9,6,0,1,0,3,9,5,5,
%T A298524 0,5,9,1,4,1,7,9,7,9,6,3,1,6,0,8,1,0,9,1,0,2,3,9,3,8,4,0,2,5,0,8,9,8,
%U A298524 8,2,4,5,2,1,2,6,0,9,0,8,7,9,8,6,5,8
%N A298524 Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.790044015672757..., s(n) = (s(n - 1) + sqrt(2))^(1/2), s(0) = 1.
%C A298524 (lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - sqrt(2).  See A298512 for a guide to related sequences.
%e A298524 (n+1)*g - s(0) - s(1) - ... - s(n) -> 1.119791807304608296546488960103955059141...
%t A298524 s[0] = 1; d = Sqrt[2]; p = 1/2;
%t A298524 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
%t A298524 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298524 N[Table[s[n], {n, 0, 30}]]
%t A298524 s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
%t A298524 RealDigits[s, 10][[1]] (* A298524 *)
%Y A298524 Cf. A298512, A298525, A298526.
%K A298524 nonn,easy,cons
%O A298524 1,4
%A A298524 _Clark Kimberling_, Feb 12 2018