A040029 Continued fraction for sqrt(35).

5, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1

Offset

0,1

References

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 97.

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 275-276.

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 (0,1).

Formula

From Amiram Eldar, Nov 12 2023: (Start)

Multiplicative with a(2^e) = 10, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 9/2^s). (End)

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

Example

5.9160797830996160425673282... = 5 + 1/(1 + 1/(10 + 1/(1 + 1/(10 + ...)))). - Harry J. Smith, Jun 04 2009

Maple

Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):

Mathematica

ContinuedFraction[Sqrt[35], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
PadRight[{5}, 120, {10, 1}] (* Harvey P. Dale, Mar 23 2021 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 22000); x=contfrac(sqrt(35)); for (n=0, 20000, write("b040029.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Crossrefs

Cf. A010490 (decimal expansion), A010691.

Sequence in context: A254068 A146070 A308504 * A105086 A305838 A329373

Adjacent sequences: A040026 A040027 A040028 * A040030 A040031 A040032

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved