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A062711
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Number of prime Gaussian integers z=a+bi with |z|<=n.
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4
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0, 1, 4, 6, 8, 10, 15, 19, 21, 25, 32, 34, 38, 44, 46, 52, 60, 66, 73, 79, 87, 93, 98, 104, 114, 122, 128, 138, 146, 154, 163, 173, 181, 193, 203, 213, 221, 231, 239, 245, 259, 273, 280, 294, 304, 316, 327, 343, 359, 369
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OFFSET
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1,3
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LINKS
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FORMULA
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Two prime Gaussian integers are not counted separately if they are associated, i.e. if their quotient is a unit (1, i, -1 or -i).
Similar to the ordinary prime number theorem (see A000720) we have the asymptotic expression: a(n) ~ n^2/(2 * log(n)) - Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 16 2001
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MATHEMATICA
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m = 50;
t = Table[x + y I, {x, -m, m}, {y, -m, m}] // Flatten[#, 1]& // Select[#, PrimeQ[#, GaussianIntegers -> True]& ]& // Sort // DeleteDuplicates[#, Abs[#1] == Abs[#2] && MatchQ[#1 /#2 , 1|-1|I|-I]& ]&;
a[n_] := Select[t, Abs[#] <= n&] // Length;
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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