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 A055028 Number of Gaussian primes of norm n. 2
 0, 0, 4, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS These are the primes in the ring of integers a+bi, a and b rational integers, i = sqrt(-1). 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 Seiichi Manyama, Table of n, a(n) for n = 0..10000 FORMULA a(n) = 4 * A055029(n). - Franklin T. Adams-Watters, May 05 2006 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] = 8; a[2] = 4; a[n_ /; (p = Sqrt[n]; PrimeQ[p] && Mod[p, 4] == 3)] = 4; a[_] = 0; Table[ a[n], {n, 0, 100}] (* Jean-François Alcover, Jul 30 2013, after Franklin T. Adams-Watters *) CROSSREFS Cf. A055025-A055029, A055664-... , A295996. Sequence in context: A255328 A321433 A016678 * A330316 A028591 A048728 Adjacent sequences:  A055025 A055026 A055027 * A055029 A055030 A055031 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 May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)