A010137 Continued fraction for sqrt(47).

6, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12

Offset

0,1

References

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 98.

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

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).

Formula

From Amiram Eldar, Nov 12 2023: (Start)

Multiplicative with a(2) = 5, a(2^e) = 12 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-2) + 7/4^s). (End)

G.f.: (6 + x + 5*x^2 + x^3 + 6*x^4)/(1 - x^4). - Stefano Spezia, Jul 27 2025

Example

6.85565460040104412493587144... = 6 + 1/(1 + 1/(5 + 1/(1 + 1/(12 + ...)))). - Harry J. Smith, Jun 06 2009

Mathematica

ContinuedFraction[Sqrt[47], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(47)); for (n=0, 20000, write("b010137.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

Crossrefs

Cf. A010501 (decimal expansion).

Sequence in context: A230821 A160135 A178645 * A245967 A212006 A245725

Adjacent sequences: A010134 A010135 A010136 * A010138 A010139 A010140

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved