A010166 Continued fraction for sqrt(95).

9, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 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) = 2, 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 + 1/4^(s-2)). (End)

Example

9.74679434480896390683841319... = 9 + 1/(1 + 1/(2 + 1/(1 + 1/(18 + ...)))). - Harry J. Smith, Jun 11 2009

Mathematica

ContinuedFraction[Sqrt[95], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 20000); x=contfrac(sqrt(95)); for (n=0, 20000, write("b010166.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 11 2009

Crossrefs

Cf. A010546 (decimal expansion).

Sequence in context: A257437 A339757 A354347 * A186116 A242627 A289502

Adjacent sequences: A010163 A010164 A010165 * A010167 A010168 A010169

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved