A010167 Continued fraction for sqrt(96).

9, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18

Offset

0,1

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac.

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 14 2023: (Start)

Multiplicative with a(2) = 3, a(2^e) = 18 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) + 15/4^s). (End)

Example

9.79795897113271239278913629... = 9 + 1/(1 + 1/(3 + 1/(1 + 1/(18 + ...)))). - Harry J. Smith, Jun 11 2009

Mathematica

ContinuedFraction[Sqrt[96], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
PadRight[{9}, 120, {18, 1, 3, 1}] (* Harvey P. Dale, Apr 14 2020 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(96)); for (n=0, 20000, write("b010167.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 11 2009

Crossrefs

Cf. A010547 (decimal expansion).

Sequence in context: A154490 A051995 A198835 * A154181 A334479 A239121

Adjacent sequences: A010164 A010165 A010166 * A010168 A010169 A010170

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved