A010173 Continued fraction for sqrt(107).

10, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..999
• 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).

Crossrefs

Cf. A177935 (decimal expansion), A041192/A041193 (convergents).

Programs

Mathematica

ContinuedFraction[Sqrt[107],300] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2011 *)

Python

from sympy import sqrt
from sympy.ntheory.continued_fraction import continued_fraction_iterator
def aupton(terms):
    gen = continued_fraction_iterator(sqrt(107))
    return [next(gen) for i in range(terms)]
print(aupton(82)) # Michael S. Branicky, Oct 02 2021

Formula

G.f.: (-10*x^6 - 2*x^5 - x^4 - 9*x^3 - x^2 - 2*x - 10)/(x^6 - 1). - Chai Wah Wu, Oct 02 2021