cp's OEIS Frontend

A298527 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 1.9078532620869538..., s(n) = (s(n - 1) + sqrt(3))^(1/2), s(0) = 2.

%I A298527 #6 Jan 10 2024 16:14:27
%S A298527 1,2,4,6,5,3,1,3,8,3,4,6,9,9,0,9,5,8,3,2,5,7,4,3,8,5,5,2,3,6,3,6,2,8,
%T A298527 3,3,5,7,5,8,0,1,3,5,9,2,0,4,9,6,8,0,5,6,7,5,2,9,6,9,1,1,6,2,0,0,7,6,
%U A298527 0,3,3,9,3,6,2,5,0,6,4,5,5,9,3,8,9,8
%N A298527 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 1.9078532620869538..., s(n) = (s(n - 1) + sqrt(3))^(1/2), s(0) = 2.
%C A298527 (lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - sqrt(3).  See A298512 for a guide to related sequences.
%e A298527 s(0) + s(1) + ... + s(n) - (n+1)*g -> 0.124653138346990958325743855236362833575...
%t A298527 s[0] = 2; d = Sqrt[3]; p = 1/2;
%t A298527 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
%t A298527 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298527 N[Table[s[n], {n, 0, 30}]]
%t A298527 s = N[Sum[- g + s[n], {n, 0, 200}], 150 ];
%t A298527 RealDigits[s, 10][[1]] (* A298527 *)
%Y A298527 Cf. A298512, A298526.
%K A298527 nonn,easy,cons
%O A298527 0,2
%A A298527 _Clark Kimberling_, Feb 12 2018