A010122 Continued fraction for sqrt(13).

3, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6

Offset

0,1

Comments

Eventual period is (1, 1, 1, 1, 6). - Zak Seidov, Mar 05 2011

References

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 96 at p. 264.

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

Formula

From Amiram Eldar, Nov 12 2023: (Start)

Multiplicative with a(5^e) = 6, and a(p^e) = 1 for p != 5.

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

G.f.: (3 + x + x^2 + x^3 + x^4 + 3*x^5)/(1 - x^5). - Stefano Spezia, Aug 17 2024

Example

3.605551275463989293119221267... = 3 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - Harry J. Smith, Jun 02 2009

Mathematica

ContinuedFraction[Sqrt[13], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 13000); x=contfrac(sqrt(13)); for (n=0, 20000, write("b010122.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009

Crossrefs

Cf. A010470 (decimal expansion).

Sequence in context: A140750 A028264 A208673 * A220693 A208615 A058663

Adjacent sequences: A010119 A010120 A010121 * A010123 A010124 A010125

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved