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Continued fraction for sqrt(114).
1

%I #33 Nov 15 2023 01:16:18

%S 10,1,2,10,2,1,20,1,2,10,2,1,20,1,2,10,2,1,20,1,2,10,2,1,20,1,2,10,2,

%T 1,20,1,2,10,2,1,20,1,2,10,2,1,20,1,2,10,2,1,20,1,2,10,2,1,20,1,2,10,

%U 2,1,20,1,2,10,2,1,20,1,2,10

%N Continued fraction for sqrt(114).

%H Vincenzo Librandi, <a href="/A010179/b010179.txt">Table of n, a(n) for n = 0..1000</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_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F G.f.: (10 + x + 2*x^2 + 10*x^3 + 2*x^4 + x^5 + 10*x^6)/(1 - x^6). - _Bruno Berselli_, Jun 13 2013

%F From _Amiram Eldar_, Nov 15 2023: (Start)

%F Multiplicative with a(2^e) = 2, a(3^e) = 10, and a(p^e) = 1 for p >= 5.

%F Dirichlet g.f.: zeta(s) * (1 + 1/2^s) * (1 + 1/3^(s-2)). (End)

%t ContinuedFraction[Sqrt[114],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 11 2011 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_