A040261 Continued fraction for sqrt(278).

16, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2, 16, 2, 1, 32, 1, 2

Offset

0,1

Links

Table of n, a(n) for n=0..80.

Index entries for continued fractions for constants.

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

Formula

From Amiram Eldar, Nov 29 2023: (Start)

Multiplicative with a(2^e) = 2, a(3^e) = 16, and a(p^e) = 1 for p >= 5.

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

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(278)), confrac);

Mathematica

ContinuedFraction[Sqrt[278], 100] (* Harvey P. Dale, Apr 04 2023 *)
(* Alternative: *)
PadRight[{16}, 100, {32, 1, 2, 16, 2, 1}] (* Harvey P. Dale, Apr 04 2023 *)

Crossrefs

Sequence in context: A040263 A082696 A040262 * A040265 A040264 A040266

Adjacent sequences: A040258 A040259 A040260 * A040262 A040263 A040264

Keyword

nonn,cofr,easy,mult,changed

Author

N. J. A. Sloane

Status

approved