A040037 - OEIS

%I #31 Nov 12 2023 06:06:00

%S 6,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,

%T 12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,

%U 12,1,1,1,2,1,1,1,12,1,1,1,2,1

%N Continued fraction for sqrt(44).

%H Harry J. Smith, <a href="/A040037/b040037.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_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).

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

%F Multiplicative with a(2) = 1, a(4) = 2, a(2^e) = 12 for e >= 3, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 5/2^(3*s-1) + 1/4^s). (End)

%e 6.633249580710799698229865473... = 6 + 1/(1 + 1/(1 + 1/(1 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 05 2009

%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

%t ContinuedFraction[Sqrt[44],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 06 2011 *)

%t PadRight[{6},80,{12,1,1,1,2,1,1,1}] (* _Harvey P. Dale_, Apr 02 2013 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 14000); x=contfrac(sqrt(44)); for (n=0, 20000, write("b040037.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 05 2009

%Y Cf. A010498 (decimal expansion).

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_