A040294 Continued fraction for sqrt(312).

17, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 1, 34, 1, 1, 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) = 1, a(2^e) = 34 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 33/4^s). (End)

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(312)), confrac);

Mathematica

ContinuedFraction[Sqrt[312], 100] (* or *) PadRight[{17}, 100, {34, 1, 1, 1}] (* Harvey P. Dale, Apr 20 2022 *)

Crossrefs

Sequence in context: A040292 A040293 A351307 * A040291 A040290 A201134

Adjacent sequences: A040291 A040292 A040293 * A040295 A040296 A040297

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved