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.

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..85.

Example

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

Mathematica

s[0] = 2; d = E; p = 1/2;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298529 *)

Crossrefs

Cf. A298512, A298528.

Sequence in context: A286982 A153595 A195482 * A245273 A199728 A199867

Adjacent sequences: A298526 A298527 A298528 * A298530 A298531 A298532

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 12 2018

Status

approved