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.

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, 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, 2, 2, 2, 8, 4, 5, 6, 3, 4, 9, 9, 7, 4, 6, 7, 4, 6, 6

Offset

1,2

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=1..86.

Example

(n+1)*g) - s(0) - s(1) - ... - s(n) -> 1.604332641724577300539659547213826891...

Mathematica

s[0] = 1; 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]] (* A298528 *)

Crossrefs

Cf. A298512, A298529.

Sequence in context: A196878 A209835 A344973 * A341325 A021947 A073010

Adjacent sequences: A298525 A298526 A298527 * A298529 A298530 A298531

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 12 2018

Status

approved