%I A053004
%S A053004 1,1,9,8,1,4,0,2,3,4,7,3,5,5,9,2,2,0,7,4,3,9,9,2,2,4,9,2,2,8,0,3,2,3,8,
%T A053004 7,8,2,2,7,2,1,2,6,6,3,2,1,5,6,5,1,5,5,8,2,6,3,6,7,4,9,5,2,9,4,6,4,0,5,
%U A053004 2,1,4,1,4,3,9,1,5,6,7,0,8,3,5,8,8,5,5,5,6,4,8,9,7,9,3,3,8,9,3,7,5,9,0
%N A053004 Decimal expansion of M(1,sqrt(2)).
%C A053004 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 A053004 J. M. Borwein and P. B. Borwein, Pi and the AGM, page 5.
%D A053004 J. R. Goldman, The Queen of Mathematics, 1998, p. 92.
%H A053004 Harry J. Smith, <a href="b053004.txt">Table of n, a(n) for n=1,...,20000</
               a>
%H A053004 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GaussConstant.html">Link to a section of The World of Mathematics.</
               a>
%e A053004 1.19814023473559220743992249228...
%o A053004 (PARI) { default(realprecision, 20080); x=agm(1, sqrt(2)); for (n=1, 
               20000, d=floor(x); x=(x-d)*10; write("b053004.txt", n, " ", d)); 
               } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 20 2009]
%Y A053004 Cf. A014549, A053002, A053003.
%Y A053004 Sequence in context: A021106 A072915 A155683 this_sequence A019888 A154975 
               A008570
%Y A053004 Adjacent sequences: A053001 A053002 A053003 this_sequence A053005 A053006 
               A053007
%K A053004 nonn,cons,nice,easy
%O A053004 1,3
%A A053004 N. J. A. Sloane (njas(AT)research.att.com), Feb 21 2000
%E A053004 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 22 2000
%E A053004 Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 19 2009