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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• mult
• changed

Examples

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

References

• 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).

Crossrefs

Cf. A010490 (decimal expansion), A010691.

Programs

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 *)

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

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