%I #35 Nov 12 2023 05:57:29
%S 3,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,
%T 1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,
%U 1,1,6,1,1,1,1,6,1,1,1,1,6
%N Continued fraction for sqrt(13).
%C Eventual period is (1, 1, 1, 1, 6). - _Zak Seidov_, Mar 05 2011
%H Harry J. Smith, <a href="/A010122/b010122.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_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F From _Amiram Eldar_, Nov 12 2023: (Start)
%F Multiplicative with a(5^e) = 6, and a(p^e) = 1 for p != 5.
%F Dirichlet g.f.: zeta(s) * (1 + 1/5^(s-1)). (End)
%e 3.605551275463989293119221267... = 3 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 02 2009
%t ContinuedFraction[Sqrt[13],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 13000); x=contfrac(sqrt(13)); for (n=0, 20000, write("b010122.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 02 2009
%Y Cf. A010470 (decimal expansion).
%K nonn,cofr,easy,mult
%O 0,1
%A _N. J. A. Sloane_
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