A040446 Continued fraction for sqrt(468).

21, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1, 42, 1, 1, 1, 2, 1, 1, 1

Offset

0,1

Links

Table of n, a(n) for n=0..87.

Index entries for continued fractions for constants.

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

Formula

From Amiram Eldar, Dec 26 2023: (Start)

Multiplicative with a(2) = 1, a(4) = 2, a(2^e) = 42 for e >= 3, and a(p^e) = 1 for an odd prime p.

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

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(468)), confrac);

Mathematica

ContinuedFraction[Sqrt[468], 100] (* or *) PadRight[{21}, 100, {42, 1, 1, 1, 2, 1, 1, 1}] (* Harvey P. Dale, Feb 28 2015 *)

Crossrefs

Sequence in context: A110454 A265156 A040445 * A040447 A040444 A040443

Adjacent sequences: A040443 A040444 A040445 * A040447 A040448 A040449

Keyword

nonn,cofr,easy,less,mult

Author

N. J. A. Sloane

Status

approved