

A228233


Number of Gaussian primes of norm less than or equal to n in the first quadrant.


4



0, 1, 5, 7, 9, 11, 17, 21, 23, 27, 35, 37, 41, 47, 49, 55, 63, 69, 77, 83, 91, 97, 103, 109, 119, 127, 133, 143, 151, 159, 169, 179, 187, 199, 209, 219, 227, 237, 245, 251, 265, 279, 287, 301, 311, 323, 335, 351, 367, 377, 385, 401, 419, 431, 441, 455, 469
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OFFSET

1,3


COMMENTS

Include 2 times the primes (once for the real axis, once for the imaginary axis).
More precisely, a(n) includes all Gaussian primes (with the appropriate norms) on the first quadrant's bounding semiaxes. All such Gaussian primes occur in pairs {p, pi} (one real and one imaginary associate), where p is a classical prime of the form 4m + 3 (so p is in A002145) and p <= n.  Rick L. Shepherd, Jun 16 2017


LINKS



MATHEMATICA

nn = 100; t = Select[Flatten[Table[a + b*I, {a, 0, nn}, {b, 0, nn}]], PrimeQ[#, GaussianIntegers > True] &]; t2 = Table[0, {nn}]; Do[f = Ceiling[Abs[i]]; If[f <= nn, t2[[f]]++], {i, t}]; Accumulate[t2] (* T. D. Noe, Aug 19 2013 *)


CROSSREFS

Cf. A000603 (number of Gaussian integers in the first quadrant with norm less than or equal to n).
Cf. A062711 (counts the Gaussian primes on only one axis).
Cf. A228232 (this sequence excluding classical primes and pure imaginary primes).
Cf. A002145 (Gaussian primes that are positive integers).


KEYWORD

nonn


AUTHOR



STATUS

approved



