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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
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
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
KEYWORD
nonn
AUTHOR
Olivier Gérard, Aug 17 2013
STATUS
approved