%I #34 Nov 12 2023 05:59:16

%S 4,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,

%T 2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,2,4,2,1,8,1,

%U 2,4,2,1,8,1,2,4,2,1,8,1,2

%N Continued fraction for sqrt(22).

%H Harry J. Smith, <a href="/A010126/b010126.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_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F From _Amiram Eldar_, Nov 12 2023: (Start)

%F Multiplicative with a(2^e) = 2, a(3^e) = 4, and a(p^e) = 1 for p >= 5.

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

%e 4.690415759823429554565630113... = 4 + 1/(1 + 1/(2 + 1/(4 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 03 2009

%t ContinuedFraction[Sqrt[22],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)

%t PadRight[{4},120,{8,1,2,4,2,1}] (* _Harvey P. Dale_, Jul 02 2019 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(22)); for (n=0, 20000, write("b010126.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009

%Y Cf. A041034/A041035 (convergents), A248250 (Egyptian fraction), A010478 (decimal expansion).

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_