Search: id:A055668
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%I A055668
%S A055668 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,
%T A055668 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,
%U A055668 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
%N A055668 Number of inequivalent Eisenstein-Jacobi primes of norm n.
%C A055668 These are the primes in the ring of integers a+b*omega, a and b rational 
               integers, omega = (1+sqrt(-3))/2.
%C A055668 Two primes are considered equivalent if they differ by multiplication 
               by a unit (+-1, +-omega, +-omega^2).
%D A055668 R. K. Guy, Unsolved Problems in Number Theory, A16.
%D A055668 L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, 
               NY, 1910, see Chap. VI.
%F A055668 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
%e A055668 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.
%Y A055668 Cf. A055664-A055667, A055025-A055029. See A004016 and A035019 for theta 
               series of Eisenstein (or hexagonal) lattice.
%Y A055668 Sequence in context: A089798 A070536 A030201 this_sequence A045839 A000086 
               A045838
%Y A055668 Adjacent sequences: A055665 A055666 A055667 this_sequence A055669 A055670 
               A055671
%K A055668 nonn,easy,nice
%O A055668 0,8
%A A055668 N. J. A. Sloane (njas(AT)research.att.com), Jun 09 2000
%E A055668 More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 05 
               2006

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