A298532 Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.866760399173862092990..., s(n) = (s(n - 1) + tau)^(1/2), s(0) = tau = (1+sqrt(5))/2 (golden ratio).

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

Offset

0,1

Comments

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

Links

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

Example

lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)) -> 0.3415333980529057321950...

Mathematica

tau = GoldenRatio;
s[0] = tau; d = tau; 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]] (* A298532 *)

Crossrefs

Cf. A298512, A298531.

Sequence in context: A079529 A361508 A299022 * A133779 A137911 A019599

Adjacent sequences: A298529 A298530 A298531 * A298533 A298534 A298535

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 13 2018

Status

approved