cp's OEIS Frontend

A298530 Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 2.3416277185114784317..., s(n) = (s(n - 1) + Pi)^(1/2), s(0) = 1.

%I A298530 #6 Jan 10 2024 16:15:36
%S A298530 1,7,3,2,6,4,4,0,7,0,0,6,1,4,8,5,8,0,4,1,2,4,7,1,6,6,6,7,2,2,1,9,6,0,
%T A298530 8,7,0,3,9,4,1,5,6,4,4,6,4,2,6,1,4,3,5,9,5,0,5,0,2,4,4,7,5,8,7,8,3,1,
%U A298530 4,2,1,7,6,9,7,6,7,4,0,0,5,9,9,3,0,8
%N A298530 Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 2.3416277185114784317..., s(n) = (s(n - 1) + Pi)^(1/2), s(0) = 1.
%C A298530 (lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - Pi.  See A298512 for a guide to related sequences.
%e A298530 lim_ {n->oo} ((n+1)*g-s(0)-s(1)-...-s(n)) -> 1.732644070061485804124716667...
%t A298530 s[0] = 1; d = Pi; p = 1/2;
%t A298530 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
%t A298530 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298530 N[Table[s[n], {n, 0, 30}]]
%t A298530 s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
%t A298530 RealDigits[s, 10][[1]] (* A298530 *)
%Y A298530 Cf. A298512, A298531.
%K A298530 nonn,easy,cons
%O A298530 1,2
%A A298530 _Clark Kimberling_, Feb 12 2018