A040411 Continued fraction for sqrt(432).

20, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 1, 40, 1, 3, 1, 1, 1, 3, 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 20 2023: (Start)

Multiplicative with a(2) = 3, a(4) = 1, a(2^e) = 40 for e >= 3, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) - 1/2^(2*s-1) + 39/2^(3*s)). (End)

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(432)), confrac);

Mathematica

ContinuedFraction[Sqrt[432], 120] (* or *) PadRight[{20}, 120, {40, 1, 3, 1, 1, 1, 3, 1}] (* Harvey P. Dale, May 22 2016 *)

Crossrefs

Sequence in context: A040409 A040408 A040407 * A040410 A040413 A040412

Adjacent sequences: A040408 A040409 A040410 * A040412 A040413 A040414

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved