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 A055666 Number of inequivalent Eisenstein-Jacobi primes of successive norms (indexed by A055664). 5
 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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). 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. VI. LINKS Jean-François Alcover, Table of n, a(n) for n = 1..1000 EXAMPLE 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. MATHEMATICA norms = Join[{3}, Select[Range[2000], (PrimeQ[#] && Mod[#, 6] == 1) || (PrimeQ[Sqrt[#]] && Mod[Sqrt[#], 3] == 2) &]]; r[n_] := Length[Reduce[n == a^2 - a*b + b^2, {a, b}, Integers]]/6; A055666 = r /@ norms (* Jean-François Alcover, Oct 24 2013 *) CROSSREFS Cf. A055664-A055668, A055025-A055029. See A004016 and A035019 for theta series of Eisenstein (or hexagonal) lattice. Sequence in context: A282625 A026498 A140685 * A251139 A195061 A064130 Adjacent sequences:  A055663 A055664 A055665 * A055667 A055668 A055669 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane, Jun 09 2000 EXTENSIONS More terms from Franklin T. Adams-Watters, May 05 2006 STATUS approved

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)