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

1,3

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 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

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).

Sequence in context: A023380 A076190 A028885 * A256091 A229064 A024910

Adjacent sequences: A228230 A228231 A228232 * A228234 A228235 A228236

Keyword

nonn

Author

Olivier Gérard, Aug 17 2013

Status

approved