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A228235
Number of Gaussian primes of norm less than or equal to n in the first quadrant on or below the first diagonal.
2
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
1,3
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).
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 *)
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).
Sequence in context: A206330 A104373 A047427 * A228895 A267322 A218929
KEYWORD
nonn
AUTHOR
Olivier Gérard, Aug 17 2013
STATUS
approved