A040300 Continued fraction for sqrt(318).

17, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1, 34, 1, 4, 1

Offset

0,1

Links

Table of n, a(n) for n=0..83.

Index entries for continued fractions for constants.

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

Formula

From Amiram Eldar, Dec 10 2023: (Start)

Multiplicative with a(2) = 4, a(2^e) = 34 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 3/2^s + 15/2^(2*s-1)). (End)

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(318)), confrac);

Mathematica

ContinuedFraction[Sqrt[318], 100] (* Harvey P. Dale, Nov 04 2012 *)
PadRight[{17}, 120, {34, 1, 4, 1}] (* Harvey P. Dale, Mar 06 2023 *)

Crossrefs

Sequence in context: A239866 A040295 A040298 * A040299 A040301 A175960

Adjacent sequences: A040297 A040298 A040299 * A040301 A040302 A040303

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved