%I A014549
%S A014549 8,3,4,6,2,6,8,4,1,6,7,4,0,7,3,1,8,6,2,8,1,4,2,9,7,3,2,7,9,9,0,4,
%T A014549 6,8,0,8,9,9,3,9,9,3,0,1,3,4,9,0,3,4,7,0,0,2,4,4,9,8,2,7,3,7,0,1,0,
%U A014549 3,6,8,1,9,9,2,7,0,9,5,2,6,4,1,1,8,6,9,6,9,1,1,6,0,3,5,1,2,7,5,3,2
%N A014549 Decimal expansion of 1 / M(1,sqrt(2)) (Gauss's constant).
%C A014549 On May 30, 1799, Gauss discovered that this number is also equal to (2/
               Pi)*Integral(1/sqrt(1-t^4),t=0..1).
%C A014549 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 A014549 J. M. Borwein and P. B. Borwein, Pi and the AGM, page 5.
%D A014549 J. R. Goldman, The Queen of Mathematics, 1998, p. 92.
%H A014549 Harry J. Smith, <a href="b014549.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A014549 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 A014549 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Arithmetic-GeometricMean.html">Arithmetic-Geometric Mean</a>
%e A014549 0.8346268416740731862814297327990468...
%o A014549 (PARI) { default(realprecision, 20080); x=10*agm(1, sqrt(2))^-1; for 
               (n=0, 20000, d=floor(x); x=(x-d)*10; write("b014549.txt", n, " ", 
               d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 20 2009]
%Y A014549 Cf. A053002, A053003, A053004.
%Y A014549 Sequence in context: A070597 A091895 A111436 this_sequence A021549 A013665 
               A110234
%Y A014549 Adjacent sequences: A014546 A014547 A014548 this_sequence A014550 A014551 
               A014552
%K A014549 nonn,cons,nice
%O A014549 0,1
%A A014549 Eric Weisstein (eric(AT)weisstein.com), N. J. A. Sloane (njas(AT)research.att.com).
%E A014549 Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 19 2009