%I A010123
%S A010123 3,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,
%T A010123 1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,
%U A010123 2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6,1,2,1,6
%N A010123 Continued fraction for sqrt(14).
%D A010123 Roger Penrose, "The Road to Reality, A complete guide to the Laws of 
               the Universe", Jonathan Cape, London, 2004, page 56. [From Olivier 
               GERARD (olivier.gerard(AT)gmail.com), May 22 2009]
%H A010123 Harry J. Smith, <a href="b010123.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A010123 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">
               Contfrac</a>
%H A010123 <a href="Sindx_Con.html#confC">Index entries for continued fractions 
               for constants</a>
%F A010123 a(n)=(1/6)*{-5*(n mod 4)+4*[(n+1) mod 4]+[(n+2) mod 4]+10*[(n+3) mod 
               4]}-3*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), 
               Jun 11 2009]
%e A010123 3.741657386773941385583748732... = 3 + 1/(1 + 1/(2 + 1/(1 + 1/(6 + ...)))) 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 02 2009]
%o A010123 (PARI) { allocatemem(932245000); default(realprecision, 15000); x=contfrac(sqrt(14)); 
               for (n=0, 20000, write("b010123.txt", n, " ", x[n+1])); } [From Harry 
               J. Smith (hjsmithh(AT)sbcglobal.net), Jun 02 2009]
%Y A010123 Cf. A010471 Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jun 02 2009]
%Y A010123 Sequence in context: A135261 A102774 A131918 this_sequence A039620 A008296 
               A140185
%Y A010123 Adjacent sequences: A010120 A010121 A010122 this_sequence A010124 A010125 
               A010126
%K A010123 nonn,cofr
%O A010123 0,1
%A A010123 N. J. A. Sloane (njas(AT)research.att.com).