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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• mult

Examples

			9.79795897113271239278913629... = 9 + 1/(1 + 1/(3 + 1/(1 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 11 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. A010547 (decimal expansion).

Programs

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 *)

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

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)