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 A055027 Number of inequivalent Gaussian primes of successive norms (indexed by A055025). 4
 1, 2, 1, 2, 2, 2, 2, 2, 1, 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, 1, 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, 2, 2, 2, 2, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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). 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. LINKS Table of n, a(n) for n=1..87. Index entries for Gaussian integers and primes EXAMPLE There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i). MATHEMATICA norms = Union[ #*Conjugate[#]& [ Select[ Flatten[ Table[a + b*I, {a, 0, 31}, {b, 0, 31}]], PrimeQ[#, GaussianIntegers -> True] &]]]; f[norm_] := (Clear[a, b]; primes = {a + b*I} /. {ToRules[ Reduce[a^2 + b^2 == norm, {a, b}, Integers]]}; primes //. {p1___, p2_, p3___, p4_, p5___} /; MatchQ[p2, (-p4 | I*p4 | -I*p4)] :> {p1, p2, p3, p5} // Length); A055027 = f /@ norms (* Jean-François Alcover, Nov 30 2012 *) CROSSREFS Cf. A055025-A055029, A055664-... Sequence in context: A297773 A043532 A043557 * A214574 A342510 A298071 Adjacent sequences: A055024 A055025 A055026 * A055028 A055029 A055030 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane, Jun 09 2000 EXTENSIONS More terms from Reiner Martin, Jul 20 2001 STATUS approved

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Last modified August 11 17:54 EDT 2024. Contains 375073 sequences. (Running on oeis4.)