A228234 Number of strict Gaussian primes of norm less than or equal to n in the first quadrant on or below the first diagonal.

0, 1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 16, 18, 21, 22, 25, 29, 32, 35, 38, 42, 45, 47, 50, 55, 59, 62, 67, 71, 75, 79, 84, 88, 94, 99, 104, 108, 113, 117, 120, 127, 134, 137, 144, 149, 155, 160, 168, 176, 181, 185, 193, 202, 208, 213, 220, 227, 233, 241, 248, 256

Offset

1,3

Comments

Strict means that one does not include the ordinary integer primes and integer primes multiplied by i.

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

Links

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

Mathematica

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

Crossrefs

Cf. A211340 (number of strict Gaussian integers in this half-quadrant).

Cf. A228235 (a version of this sequence including the real axis).

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

Sequence in context: A032955 A375581 A320848 * A360792 A060526 A301599

Adjacent sequences: A228231 A228232 A228233 * A228235 A228236 A228237

Keyword

nonn

Author

Olivier Gérard, Aug 17 2013

Status

approved