A010144 Continued fraction for sqrt(59).

7, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2

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 (0,0,0,0,0,1).

Formula

From Amiram Eldar, Nov 13 2023: (Start)

Multiplicative with a(2^e) = 2, a(3^e) = 7, and a(p^e) = 1 for p >= 5.

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

Example

7.681145747868608175769687021... = 7 + 1/(1 + 1/(2 + 1/(7 + 1/(2 + ...)))). - Harry J. Smith, Jun 07 2009

Mathematica

ContinuedFraction[Sqrt[59], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
PadRight[{7}, 120, {14, 1, 2, 7, 2, 1}] (* Harvey P. Dale, May 15 2017 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(59)); for (n=0, 20000, write("b010144.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009

Crossrefs

Cf. A010512 (decimal expansion).

Sequence in context: A238273 A155773 A215670 * A195409 A318353 A354639

Adjacent sequences: A010141 A010142 A010143 * A010145 A010146 A010147

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved