%I A053003
%S A053003 1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,8,36,1,2,5,2,1,1,2,2,6,9,1,1,1,3,1,
%T A053003 2,6,1,5,1,1,2,1,13,2,2,5,1,2,2,1,5,1,3,1,3,1,2,2,2,2,8,3,1,2,2,1,10,2,
%U A053003 2,2,3,3,1,7,1,8,3,1,1,1,1,1,1,1,1,5,2,1,2,17,1,4,31,2,2,5,30,1,8,2,1
%N A053003 Continued fraction for M(1,sqrt(2)).
%C A053003 M(a,b) is the limit of the arithmetic-geometric mean iteration applied 
               repeatedly starting with a and b: a_0=a, b_0=b, a_{n+1}=(a_n+b_n)/
               2, b_{n+1}=sqrt(a_n*b_n).
%D A053003 J. M. Borwein and P. B. Borwein, Pi and the AGM, page 5.
%D A053003 J. R. Goldman, The Queen of Mathematics, 1998, p. 92.
%H A053003 Harry J. Smith, <a href="b053003.txt">Table of n, a(n) for n=1,...,20000</
               a>
%H A053003 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GaussConstant.html">Link to a section of The World of Mathematics.</
               a>
%H A053003 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">
               Contfrac</a>
%H A053003 <a href="Sindx_Con.html#confC">Index entries for continued fractions 
               for constants</a>
%e A053003 1.19814023473559220743992249228...
%o A053003 (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(agm(1, 
               sqrt(2))); for (n=1, 20000, write("b053003.txt", n, " ", x[n])); 
               } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 20 2009]
%Y A053003 Cf. A014549, A053002, A053004.
%Y A053003 Sequence in context: A156148 A156824 A053002 this_sequence A167202 A165204 
               A043053
%Y A053003 Adjacent sequences: A053000 A053001 A053002 this_sequence A053004 A053005 
               A053006
%K A053003 nonn,cofr,nice,easy
%O A053003 1,2
%A A053003 N. J. A. Sloane (njas(AT)research.att.com), Feb 21 2000
%E A053003 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 22 2000