A010179 Continued fraction for sqrt(114).

10, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10, 2, 1, 20, 1, 2, 10

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

G. Xiao, Contfrac.

Index entries for continued fractions for constants.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Formula

G.f.: (10 + x + 2*x^2 + 10*x^3 + 2*x^4 + x^5 + 10*x^6)/(1 - x^6). - Bruno Berselli, Jun 13 2013

From Amiram Eldar, Nov 15 2023: (Start)

Multiplicative with a(2^e) = 2, a(3^e) = 10, and a(p^e) = 1 for p >= 5.

Dirichlet g.f.: zeta(s) * (1 + 1/2^s) * (1 + 1/3^(s-2)). (End)

Mathematica

ContinuedFraction[Sqrt[114], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2011 *)

Crossrefs

Sequence in context: A090555 A283393 A359736 * A174209 A366165 A010181

Adjacent sequences: A010176 A010177 A010178 * A010180 A010181 A010182

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved