A040867 Continued fraction for sqrt(897).

29, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18, 1, 58, 1, 18

Offset

0,1

Links

Table of n, a(n) for n=0..74.

Index entries for continued fractions for constants.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Formula

a(n) = a(n-4) for n > 4 with a(0) = 29, a(1) = a(3) = 1, a(2) = 18, a(4) = 58. - Wesley Ivan Hurt, Dec 31 2023

From Amiram Eldar, Jan 17 2024: (Start)

Multiplicative with a(2) = 18, a(2^e) = 58 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 17/2^s + 5/2^(2*s-3)). (End)

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(897)), confrac);

Mathematica

ContinuedFraction[Sqrt[897], 80] (* or *) PadRight[{29}, 80, {58, 1, 18, 1}] (* Harvey P. Dale, Oct 14 2013 *)

Crossrefs

Sequence in context: A040864 A040865 A040866 * A040868 A169980 A040869

Adjacent sequences: A040864 A040865 A040866 * A040868 A040869 A040870

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved