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 A055029 Number of inequivalent Gaussian primes of norm n. 14
 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; refs; listen; history; text; internal format)
 OFFSET 0,6 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 Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA 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. - Franklin T. Adams-Watters, May 05 2006 a(n) = if n = 2 then 1 else 2*A079260(n) + A079261(A037213(n)). - Reinhard Zumkeller, Nov 11 2012 EXAMPLE There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i). MATHEMATICA a[n_ /; PrimeQ[n] && Mod[n, 4] == 1] = 2; a[2] = 1; a[n_ /; (p = Sqrt[n]; PrimeQ[p] && Mod[p, 4] == 3)] = 1; a[_] = 0; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 25 2011, after Franklin T. Adams-Watters *) PROG (Haskell) a055029 2 = 1 a055029 n = 2 * a079260 n + a079261 (a037213 n) -- Reinhard Zumkeller, Nov 11 2012 (PARI) a(n)=if(isprime(n), if(n%4==1, 2, n==2), if(issquare(n, &n) && isprime(n) && n%4==3, 1, 0)) \\ Charles R Greathouse IV, Feb 07 2017 CROSSREFS Cf. A055025, A055026, A055027, A055028. Cf. A055664, A055665, A055666, A055667, A055668. Sequence in context: A059483 A067618 A279255 * A126812 A008442 A327169 Adjacent sequences:  A055026 A055027 A055028 * A055030 A055031 A055032 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane, Jun 09 2000 EXTENSIONS More terms from Reiner Martin (reinermartin(AT)hotmail.com), Jul 20 2001 STATUS approved

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Last modified June 7 04:32 EDT 2020. Contains 334836 sequences. (Running on oeis4.)