A228235 - OEIS

%I #12 Apr 25 2024 14:34:11

%S 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,

%T 64,67,72,76,80,85,90,94,100,105,110,114,119,123,126,133,140,144,151,

%U 156,162,168,176,184,189,193,201,210,216,221,228,235,241,250,257

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

%C 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.

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

%H T. D. Noe, <a href="/A228235/b228235.txt">Table of n, a(n) for n = 1..1000</a>

%t 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 *)

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

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

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

%K nonn

%O 1,3

%A _Olivier Gérard_, Aug 17 2013