A040418 Continued fraction for sqrt(439).

20, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19, 1, 40, 1, 19

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

From Amiram Eldar, Dec 26 2023: (Start)

Multiplicative with a(2) = 19, a(2^e) = 40 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 9/2^(s-1) + 21/2^(2*s)). (End)

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(439)), confrac);

Mathematica

ContinuedFraction[Sqrt[439], 120] (* or *) PadRight[{20}, 120, {40, 1, 19, 1}] (* Harvey P. Dale, Jun 24 2018 *)

Crossrefs

Sequence in context: A040417 A278414 A003833 * A140116 A084923 A141589

Adjacent sequences: A040415 A040416 A040417 * A040419 A040420 A040421

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved