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%I #34 Apr 20 2020 10:52:53
%S 5,37,317,3149,31417,314197,3141549,31416025,314159053,3141592409,
%T 31415925457,314159264013,3141592649625,31415926532017,
%U 314159265350589,3141592653588533,31415926535867961,314159265358987341,3141592653589764829,31415926535897744669
%N Number of Cartesian lattice points in or on the circle x^2 + y^2 = 10^n.
%C a(n) ~ Pi*10^n [Shanks, page 164]. "Gauss gave [a(2)] = 317 and [a(4)] = 31417." [Shanks, page 165].
%D Daniel Shanks, "Solved and Unsolved Problems in Number Theory," Fourth Edition, Chelsea Publishing Co., NY, 1993, pages 164-165 and 234 [gives a(n) for n = 8, 10, 12, 14].
%D Wolfram Research, Mathematica 4, Standard Add-On Packages, Wolfram Media, Inc., Champaign, Il, 1999, pages 322-3.
%H Hiroaki Yamanouchi, <a href="/A068785/b068785.txt">Table of n, a(n) for n = 0..36</a>
%H <a href="/index/Qua#quadpop">Index entries for sequences related to populations of quadratic forms</a>
%F a(n) = Sum_{k=0..10^n} A004018(k). - _Robert Israel_, Jul 13 2014
%t k = 1; s = 1; Do[s = s + SquaresR[2, n]; If[n == 10^k, k++; Print[s]], {n, 1, 10^6} ]
%Y Cf. A004018, A057961, A057655.
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Mar 07 2002
%E Definition and comments corrected by _Jonathan Sondow_, Dec 28 2012
%E a(0) corrected and a(9)-a(19) from _Hiroaki Yamanouchi_, Jul 13 2014
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