A040204 Continued fraction for sqrt(219).

14, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 1, 28, 1, 3, 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, Nov 29 2023: (Start)

Multiplicative with a(2) = 3, a(2^e) = 28 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) + 25/4^s). (End)

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(219)), confrac);

Mathematica

ContinuedFraction[Sqrt[219], 100] (* or *) PadRight[{14}, 100, {28, 1, 3, 1}] (* Harvey P. Dale, Nov 20 2022 *)

Crossrefs

Sequence in context: A040201 A179948 A160495 * A040203 A040205 A171693

Adjacent sequences: A040201 A040202 A040203 * A040205 A040206 A040207

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved