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

0,1

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).

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A198546 A160579 A134897 * A097528 A065416 A093312

Adjacent sequences: A010156 A010157 A010158 * A010160 A010161 A010162

Keyword

nonn,cofr

Author

N. J. A. Sloane

Status

approved