A010170 Continued fraction for sqrt(99).

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

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 (0,1).

Formula

a(n+1) = 18^n mod 19, for all n >= 0. - M. F. Hasler, Mar 10 2011

From Amiram Eldar, Nov 14 2023: (Start)

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

Dirichlet g.f.: zeta(s) * (1 + 17/2^s). (End)

Example

9.9498743710661995473447982... = 9 + 1/(1 + 1/(18 + 1/(1 + 1/(18 + ...)))). - Harry J. Smith, Jun 12 2009

Mathematica

ContinuedFraction[Sqrt[99], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
PadRight[{9}, 120, {18, 1}] (* Harvey P. Dale, Aug 30 2021 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 27000); x=contfrac(sqrt(99)); for (n=0, 20000, write("b010170.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 12 2009

Crossrefs

Cf. A010550 (decimal expansion).

Sequence in context: A014721 A054018 A342637 * A317051 A013616 A205381

Adjacent sequences: A010167 A010168 A010169 * A010171 A010172 A010173

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved