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%I #27 Nov 15 2023 01:15:35
%S 9,1,3,1,18,1,3,1,18,1,3,1,18,1,3,1,18,1,3,1,18,1,3,1,18,1,3,1,18,1,3,
%T 1,18,1,3,1,18,1,3,1,18,1,3,1,18,1,3,1,18,1,3,1,18,1,3,1,18,1,3,1,18,
%U 1,3,1,18,1,3,1,18,1,3,1,18
%N Continued fraction for sqrt(96).
%H Harry J. Smith, <a href="/A010167/b010167.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_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F From _Amiram Eldar_, Nov 14 2023: (Start)
%F Multiplicative with a(2) = 3, a(2^e) = 18 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) + 15/4^s). (End)
%e 9.79795897113271239278913629... = 9 + 1/(1 + 1/(3 + 1/(1 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 11 2009
%t ContinuedFraction[Sqrt[96],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 10 2011 *)
%t PadRight[{9},120,{18,1,3,1}] (* _Harvey P. Dale_, Apr 14 2020 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(96)); for (n=0, 20000, write("b010167.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 11 2009
%Y Cf. A010547 (decimal expansion).
%K nonn,cofr,easy,mult
%O 0,1
%A _N. J. A. Sloane_
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