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Search: id:A055029
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| A055029 |
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Number of inequivalent Gaussian primes of norm n. |
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+0
13
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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; listen)
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OFFSET
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0,6
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COMMENT
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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
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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
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Index entries for Gaussian integers and primes
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FORMULA
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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
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There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i).
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CROSSREFS
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Cf. A055025-A055028, A055664-...
Sequence in context: A056170 A059483 A067618 this_sequence A126812 A008442 A086076
Adjacent sequences: A055026 A055027 A055028 this_sequence A055030 A055031 A055032
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Jun 09 2000
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EXTENSIONS
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More terms from Reiner Martin (reinermartin(AT)hotmail.com), Jul 20 2001
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