A010159 Continued fraction for sqrt(86).

9, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

Examples

			9.273618495495703752516416073... = 9 + 1/(3 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 10 2009
		

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 (0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A010537 (decimal expansion). - Harry J. Smith, Jun 10 2009

Programs

Mathematica

ContinuedFraction[Sqrt[86],300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)
PadRight[{9},120,{18,3,1,1,1,8,1,1,1,3}] (* Harvey P. Dale, Dec 13 2018 *)

Python

from sympy import sqrt
from sympy.ntheory.continued_fraction import continued_fraction_iterator
def aupton(terms):
    gen = continued_fraction_iterator(sqrt(86))
    return [next(gen) for i in range(terms)]
print(aupton(78)) # Michael S. Branicky, Sep 03 2021