cp's OEIS Frontend

A298528 Decimal expansion of lim_{n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 2.22287022972104..., s(n) = (s(n - 1) + e)^(1/2), s(0) = 1.

%I A298528 #11 Nov 24 2024 03:27:43
%S A298528 1,6,0,4,3,3,2,6,4,1,7,2,4,5,7,7,3,0,0,5,3,9,6,5,9,5,4,7,2,1,3,8,2,6,
%T A298528 8,9,1,7,6,3,8,0,8,8,1,1,2,8,3,2,3,0,8,2,9,2,5,4,1,4,7,0,9,2,8,9,7,9,
%U A298528 2,2,2,8,4,5,6,3,4,9,9,7,4,6,7,4,6,6
%N A298528 Decimal expansion of lim_{n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 2.22287022972104..., s(n) = (s(n - 1) + e)^(1/2), s(0) = 1.
%C A298528 Limit_{n->oo} s(n) = g = positive zero of x^2 - x - e. See A298512 for a guide to related sequences.
%e A298528 1.604332641724577300539659547213826891...
%t A298528 s[0] = 1; d = E; p = 1/2;
%t A298528 g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
%t A298528 s[n_] := s[n] = (s[n - 1] + d)^p
%t A298528 N[Table[s[n], {n, 0, 30}]]
%t A298528 s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
%t A298528 RealDigits[s, 10][[1]] (* A298528 *)
%Y A298528 Cf. A298512, A298529.
%K A298528 nonn,easy,cons
%O A298528 1,2
%A A298528 _Clark Kimberling_, Feb 12 2018