A298522 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = 1.86676039917386..., s(n) = (s(n - 1) + (1+sqrt(5))/2)^(1/2), s(0) = 1.

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

Offset

1,2

Comments

(lim_ {n->oo} s(n)) = g = real zero of x^2 - x - (1+sqrt(5))/2. 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)) -> 1.20829379722676782518591549956095278...

Mathematica

s[0] = 1; d = GoldenRatio; 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]] (* A298522 *)

Crossrefs

Cf. A298512, A298523.

Sequence in context: A159810 A199268 A268499 * A206436 A146543 A179990

Adjacent sequences: A298519 A298520 A298521 * A298523 A298524 A298525

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 12 2018

Status

approved