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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• mult

Examples

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

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).

Crossrefs

Cf. A010549 (decimal expansion).

Programs

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 *)

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

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)