A228233 Number of Gaussian primes of norm less than or equal to n in the first quadrant.

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

Offset: 1

Author

Olivier Gérard, Aug 17 2013

Keywords

• nonn

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 semi-axes. 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

• T. D. Noe, Table of n, a(n) for n = 1..1000

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).

Programs

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 *)