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A055029
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Number of inequivalent Gaussian primes of norm n.
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12
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0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| These are the primes in the ring of integers a+bi, a and b rational integers, i = sqrt(-1).
Two primes are considered equivalent if they differ by multiplication by a unit (+-1, +-i).
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, A16.
L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. V.
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LINKS
| Index entries for Gaussian integers and primes
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FORMULA
| a(n) = 2 if n is a prime = 1 (mod 4); a(n) = 1 if n is 2, or p^2 where p is a prime = 3 (mod 4); a(n) = 0 otherwise. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 05 2006
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EXAMPLE
| There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i).
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MATHEMATICA
| a[n_ /; PrimeQ[n] && Mod[n, 4] == 1] = 2; a[2] = 1; a[n_ /; (p = Sqrt[n]; PrimeQ[p] && Mod[p, 4] == 3)] = 1; a[_] = 0; Table[a[n], {n, 0, 100}] (* From Jean-François Alcover, Oct 25 2011, after Frank Adams-Watters *)
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CROSSREFS
| Cf. A055025-A055028, A055664-...
Sequence in context: A056170 A059483 A067618 * A126812 A008442 A086076
Adjacent sequences: A055026 A055027 A055028 * A055030 A055031 A055032
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 09 2000
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EXTENSIONS
| More terms from Reiner Martin (reinermartin(AT)hotmail.com), Jul 20 2001
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