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

0,1

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).

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A040097 A010174 A073755 * A357339 A259712 A343103

Adjacent sequences: A010170 A010171 A010172 * A010174 A010175 A010176

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved