A010169 Continued fraction for sqrt(98).

9, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 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 Wesley Ivan Hurt, Jun 23 2021: (Start)

a(n) = a(n-4).

a(0) = 9; a(n) = 7 + 6*(-1)^n + 5*cos(n*Pi/2) for n > 0. (End)

From Amiram Eldar, Nov 14 2023: (Start)

Multiplicative with a(2) = 8, a(2^e) = 18 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 7/2^s + 5/2^(2*s-1)). (End)

Example

9.89949493661166534161182106... = 9 + 1/(1 + 1/(8 + 1/(1 + 1/(18 + ...)))). - Harry J. Smith, Jun 12 2009

Mathematica

ContinuedFraction[Sqrt[98], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
PadRight[{9}, 120, {18, 1, 8, 1}] (* Harvey P. Dale, Dec 13 2015 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 24000); x=contfrac(sqrt(98)); for (n=0, 20000, write("b010169.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 12 2009

Crossrefs

Cf. A010549 (decimal expansion).

Sequence in context: A371856 A182494 A065444 * A113657 A098783 A234468

Adjacent sequences: A010166 A010167 A010168 * A010170 A010171 A010172

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved