A228235 Number of Gaussian primes of norm less than or equal to n in the first quadrant on or below the first diagonal.

0, 1, 3, 4, 5, 6, 9, 11, 12, 14, 18, 19, 21, 24, 25, 28, 32, 35, 39, 42, 46, 49, 52, 55, 60, 64, 67, 72, 76, 80, 85, 90, 94, 100, 105, 110, 114, 119, 123, 126, 133, 140, 144, 151, 156, 162, 168, 176, 184, 189, 193, 201, 210, 216, 221, 228, 235, 241, 250, 257

Offset: 1

Author

Olivier Gérard, Aug 17 2013

Keywords

• nonn

Comments

In the first quadrant and on or below the first diagonal, means here that the imaginary part is nonnegative and inferior or equal to the real part.

The norm used is the absolute value of the Gaussian integers, seen as complex numbers : sqrt( re(z)^2 + im(z)^2).

Links

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

Crossrefs

Cf. A228172 (number of Gaussian integers in this half-quadrant).

Cf. A228234 (version of this sequence excluding the real axis).

Cf. A228232, A228233 (versions counting the whole first quadrant).

Programs

Mathematica

nn = 100; t = Select[Flatten[Table[a + b*I, {a, 0, nn}, {b, a, 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 *)