A040451 Continued fraction for sqrt(473).

21, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 1, 42, 1, 2, 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 26 2023: (Start)

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

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

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(473)), confrac);

Mathematica

ContinuedFraction[Sqrt[473], 120] (* or *) PadRight[{21}, 120, {42, 1, 2, 1}] (* Harvey P. Dale, May 15 2021 *)

Crossrefs

Sequence in context: A015147 A174945 A040450 * A040449 A040448 A040453

Adjacent sequences: A040448 A040449 A040450 * A040452 A040453 A040454

Keyword

nonn,cofr,easy,less,mult

Author

N. J. A. Sloane

Status

approved