%I A040003
%S A040003 2,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,
%T A040003 2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,
%U A040003 4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4
%N A040003 Continued fraction for sqrt(6).
%H A040003 Harry J. Smith, <a href="b040003.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A040003 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">
               Contfrac</a>
%H A040003 <a href="Sindx_Con.html#confC">Index entries for continued fractions 
               for constants</a>
%F A040003 a(n)=3+(-1)^n-2*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), 
               Jun 11 2009]
%e A040003 2.449489742783178098197284074... = 2 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + ...)))) 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
%p A040003 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%o A040003 (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(6)); 
               for (n=0, 20000, write("b040003.txt", n, " ", x[n+1])); } [From Harry 
               J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
%Y A040003 Cf. A010464 Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jun 01 2009]
%Y A040003 Sequence in context: A054763 A100374 A045841 this_sequence A106469 A082508 
               A163824
%Y A040003 Adjacent sequences: A040000 A040001 A040002 this_sequence A040004 A040005 
               A040006
%K A040003 nonn,cofr,easy
%O A040003 0,1
%A A040003 N. J. A. Sloane (njas(AT)research.att.com).