A298517 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = (1 + sqrt (13))/2, s(n) = (s(n - 1) + 3)^(1/2), s(0) = 1.

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

Offset

0,2

Comments

(lim_ {n->oo} s(n)) = g = (1 + sqrt (13))/2. See A298512 for a guide to related sequences.

Links

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

Example

((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 0.91504984801513491484363121460300...

Mathematica

s[0] = 1; d = 3; p = 1/2; s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
z = 200 ; g = (1 + Sqrt[13])/2;
s = N[(z + 1)*g - Sum[s[n], {n, 0, z}], 150 ];
RealDigits[s, 10][[1]];  (* A298517 *)

Crossrefs

Cf. A298512, A298515, A298516.

Sequence in context: A242760 A196607 A200015 * A199451 A135154 A285832

Adjacent sequences: A298514 A298515 A298516 * A298518 A298519 A298520

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 11 2018

Status

approved