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A068785
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Number of Cartesian lattice points in or on the circle x^2 + y^2 = 10^n.
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11
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5, 37, 317, 3149, 31417, 314197, 3141549, 31416025, 314159053, 3141592409, 31415925457, 314159264013, 3141592649625, 31415926532017, 314159265350589, 3141592653588533, 31415926535867961, 314159265358987341, 3141592653589764829, 31415926535897744669
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OFFSET
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0,1
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COMMENTS
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a(n) ~ Pi*10^n [Shanks, page 164]. "Gauss gave [a(2)] = 317 and [a(4)] = 31417." [Shanks, page 165].
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REFERENCES
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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].
Wolfram Research, Mathematica 4, Standard Add-On Packages, Wolfram Media, Inc., Champaign, Il, 1999, pages 322-3.
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LINKS
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FORMULA
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MATHEMATICA
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k = 1; s = 1; Do[s = s + SquaresR[2, n]; If[n == 10^k, k++; Print[s]], {n, 1, 10^6} ]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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