A010153 - OEIS

%I #34 Oct 05 2024 17:44:25

%S 8,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,

%T 1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,

%U 1,1,1,16,1,1,1,16,1,1,1,16

%N Continued fraction for sqrt(75) (or 5*sqrt(3)).

%H Harry J. Smith, <a href="/A010153/b010153.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 13 2023: (Start)

%F Multiplicative with a(2) = 1, a(2^e) = 16 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 15/4^s). (End)

%e 8.66025403784438646763723170... = 8 + 1/(1 + 1/(1 + 1/(1 + 1/(16 + ...)))). - _Harry J. Smith_, Jun 02 2009

%t ContinuedFraction[Sqrt[75],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 08 2011 *)

%t PadRight[{8},120,{16,1,1,1}] (* _Harvey P. Dale_, Oct 05 2024 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(75)); for (n=0, 20000, write("b010153.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 02 2009

%Y Cf. A010527.

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_