login
Continued fraction for sqrt(135).
1

%I #29 Nov 15 2023 01:12:34

%S 11,1,1,1,1,1,1,1,22,1,1,1,1,1,1,1,22,1,1,1,1,1,1,1,22,1,1,1,1,1,1,1,

%T 22,1,1,1,1,1,1,1,22,1,1,1,1,1,1,1,22,1,1,1,1,1,1,1,22,1,1,1,1,1,1,1,

%U 22,1,1,1,1,1,1,1,22,1,1,1,1

%N Continued fraction for sqrt(135).

%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_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).

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

%F Multiplicative with a(2^e) = 1 if e <=2 and 22 otherwise, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 21/8^s). (End)

%t ContinuedFraction[Sqrt[135],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 12 2011 *)

%t PadRight[{11},120,{22,1,1,1,1,1,1,1}] (* _Harvey P. Dale_, Feb 24 2018 *)

%Y Cf. A140248.

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_