A010159 - OEIS

%I #33 Dec 27 2023 00:18:56

%S 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,

%T 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,

%U 1,1,1,3,18,3,1,1,1,8,1,1

%N Continued fraction for sqrt(86).

%H Harry J. Smith, <a href="/A010159/b010159.txt">Table of n, a(n) for n = 0..20000</a>

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1).

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

%t ContinuedFraction[Sqrt[86],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 09 2011 *)

%t PadRight[{9},120,{18,3,1,1,1,8,1,1,1,3}] (* _Harvey P. Dale_, Dec 13 2018 *)

%o (Python)

%o from sympy import sqrt

%o from sympy.ntheory.continued_fraction import continued_fraction_iterator

%o def aupton(terms):

%o     gen = continued_fraction_iterator(sqrt(86))

%o     return [next(gen) for i in range(terms)]

%o print(aupton(78)) # _Michael S. Branicky_, Sep 03 2021

%Y Cf. A010537 (decimal expansion). - _Harry J. Smith_, Jun 10 2009

%K nonn,cofr

%O 0,1

%A _N. J. A. Sloane_