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Search: id:A055668
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| A055668 |
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Number of inequivalent Eisenstein-Jacobi primes of norm n. |
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+0
6
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| 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0
(list; graph; listen)
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OFFSET
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0,8
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COMMENT
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These are the primes in the ring of integers a+b*omega, a and b rational integers, omega = (1+sqrt(-3))/2.
Two primes are considered equivalent if they differ by multiplication by a unit (+-1, +-omega, +-omega^2).
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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. VI.
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FORMULA
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a(n) = 2 if n is a prime = 1 (mod 6); a(n) = 1 if n = 3 or n = p^2 where p is a prime = 2 (mod 3); 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 6 Eisenstein-Jacobi primes of norm 3, omega-omega^2 times one of the 6 units [ +-1, +-omega, +-omega^2 ] but only one up to equivalence.
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CROSSREFS
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Cf. A055664-A055667, A055025-A055029. See A004016 and A035019 for theta series of Eisenstein (or hexagonal) lattice.
Sequence in context: A089798 A070536 A030201 this_sequence A045839 A000086 A045838
Adjacent sequences: A055665 A055666 A055667 this_sequence A055669 A055670 A055671
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 09 2000
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EXTENSIONS
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More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 05 2006
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