cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A068785 Number of Cartesian lattice points in or on the circle x^2 + y^2 = 10^n.

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