A298529 - OEIS

A298529

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

%I #6 Jan 10 2024 16:15:15

%S 6,3,5,5,7,1,9,6,9,3,6,9,9,3,8,4,5,2,0,3,1,9,6,1,8,4,2,0,9,8,6,7,7,7,

%T 5,4,8,1,3,5,4,6,5,2,9,2,0,5,2,1,4,4,3,9,2,0,2,3,3,9,4,4,1,1,1,4,4,2,

%U 2,6,8,4,0,3,9,0,4,9,8,7,9,3,7,7,9,3

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

%C (lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - e. See A298512 for a guide to related sequences.

%e s(0) + s(1) + ... + s(n) - (n+1)*g -> 0.6355719693699384520319618420986777...

%t s[0] = 2; d = E; p = 1/2;

%t g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]

%t s[n_] := s[n] = (s[n - 1] + d)^p

%t N[Table[s[n], {n, 0, 30}]]

%t s = N[Sum[g - s[n], {n, 0, 200}], 150 ];

%t RealDigits[s, 10][[1]] (* A298529 *)

%Y Cf. A298512, A298528.

%K nonn,easy,cons

%O 0,1

%A _Clark Kimberling_, Feb 12 2018