A040533 Continued fraction for sqrt(557).

23, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1, 46, 1, 1, 1, 1

Offset

0,1

Links

Table of n, a(n) for n=0..84.

Index entries for continued fractions for constants.

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

Formula

a(n) = 1 + 45*(floor(n/5) - floor((n-1)/5)) for n>0 with a(0) = 23. - Wesley Ivan Hurt, Apr 09 2017

From Amiram Eldar, Dec 26 2023: (Start)

Multiplicative with a(5^e) = 46, and a(p^e) = 1 for p != 5.

Dirichlet g.f.: zeta(s) * (1 + 9/5^(s-1)). (End)

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(557)), confrac);

Mathematica

ContinuedFraction[Sqrt[557], 100] (* Amiram Eldar, Dec 26 2023 *)

Prog

(PARI) contfrac(sqrt(557)) \\ Michel Marcus, Apr 09 2017

Crossrefs

Sequence in context: A114784 A141517 A040534 * A191816 A040535 A040536

Adjacent sequences: A040530 A040531 A040532 * A040534 A040535 A040536

Keyword

nonn,cofr,easy,less,mult

Author

N. J. A. Sloane

Status

approved