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%I #30 Nov 12 2023 06:04:22
%S 5,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,
%T 1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,1,4,1,10,
%U 1,4,1,10,1,4,1,10,1,4,1,10
%N Continued fraction for sqrt(34).
%H Harry J. Smith, <a href="/A010132/b010132.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 12 2023: (Start)
%F Multiplicative with a(2) = 4, a(2^e) = 10 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F Dirichlet g.f.: zeta(s) * (1 + 3/2^(2*s-1) + 3/2^s). (End)
%e 5.83095189484530047087415287... = 5 + 1/(1 + 1/(4 + 1/(1 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009
%t ContinuedFraction[Sqrt[34],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 06 2011 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 19000); x=contfrac(sqrt(34)); for (n=0, 20000, write("b010132.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 04 2009
%Y Cf. A010489 (decimal expansion).
%K nonn,cofr,easy,mult
%O 0,1
%A _N. J. A. Sloane_
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