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 A055026 Number of Gaussian primes of successive norms (indexed by A055025). 5
 4, 8, 4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 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 m = 32; Length /@ Split[Sort[Select[Flatten[Table[{a^2 + b^2, a + b*I}, {a, -m, m}, {b, -m, m}], 1], PrimeQ[#[[2]], GaussianIntegers -> True] & ]], #1[[1]] == #2[[1]] & ][[1 ;; 87]] (* Jean-François Alcover, Apr 08 2011 *) CROSSREFS Cf. A055025-A055029, A055664-... Sequence in context: A010713 A105398 A005883 * A336818 A205681 A059163 Adjacent sequences: A055023 A055024 A055025 * A055027 A055028 A055029 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 23:45 EDT 2024. Contains 375082 sequences. (Running on oeis4.)