A010197 Continued fraction for sqrt(138).

11, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1, 22, 1, 2, 1

Offset

0,1

Links

Table of n, a(n) for n=0..71.

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 15 2023: (Start)

Multiplicative with a(2) = 2, a(2^e) = 22 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/2^s + 5/4^(s-1)). (End)

a(n) = a(n-4) for n>4 with a(0)=11, a(1) = a(3) = 1, a(2) = 2, a(4) = 22. - Wesley Ivan Hurt, Dec 31 2023

Mathematica

ContinuedFraction[Sqrt[138], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 13 2011 *)

Crossrefs

Sequence in context: A015125 A290552 A159861 * A010196 A039617 A229186

Adjacent sequences: A010194 A010195 A010196 * A010198 A010199 A010200

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved