A040207 Continued fraction for sqrt(222).

14, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 1, 28, 1, 8, 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) = 8, a(2^e) = 28 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 7/2^s + 5/4^(s-1)). (End)

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(222)), confrac);

Mathematica

ContinuedFraction[Sqrt[222], 120] (* or *) PadRight[{14}, 120, {28, 1, 8, 1}] (* Harvey P. Dale, Jun 06 2020 *)

Crossrefs

Sequence in context: A235704 A229199 A040206 * A036163 A040208 A097181

Adjacent sequences: A040204 A040205 A040206 * A040208 A040209 A040210

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved