A010166 - OEIS

%I #25 Nov 15 2023 01:15:48

%S 9,1,2,1,18,1,2,1,18,1,2,1,18,1,2,1,18,1,2,1,18,1,2,1,18,1,2,1,18,1,2,

%T 1,18,1,2,1,18,1,2,1,18,1,2,1,18,1,2,1,18,1,2,1,18,1,2,1,18,1,2,1,18,

%U 1,2,1,18,1,2,1,18,1,2,1,18

%N Continued fraction for sqrt(95).

%H Harry J. Smith, <a href="/A010166/b010166.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) = 2, 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 + 1/4^(s-2)). (End)

%e 9.74679434480896390683841319... = 9 + 1/(1 + 1/(2 + 1/(1 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 11 2009

%t ContinuedFraction[Sqrt[95],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 10 2011 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 20000); x=contfrac(sqrt(95)); for (n=0, 20000, write("b010166.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 11 2009

%Y Cf. A010546 (decimal expansion).

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_