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Number of Gaussian primes (in the first half-quadrant; i.e., 0 to 45 degrees) with real part <= n.
2

%I #12 Apr 03 2022 01:30:22

%S 1,2,4,5,7,9,11,14,15,19,22,23,27,30,33,36,40,43,48,54,56,60,66,69,76,

%T 82,86,90,94,98,106,112,117,123,131,136,142,149,152,161,166,171,180,

%U 188,195,204,211,218,228,236

%N Number of Gaussian primes (in the first half-quadrant; i.e., 0 to 45 degrees) with real part <= n.

%D Mark A. Herkommer, "Number Theory, A Programmer's Guide," McGraw-Hill, New York, 1999, page 269.

%H T. D. Noe, <a href="/A057352/b057352.txt">Table of n, a(n) for n=1..10000</a>

%H <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>

%t c = 0; Do[ Do[ If[ PrimeQ[ j + k*I, GaussianIntegers -> True ], c++ ], {j, n, n}, {k, 0, j} ]; Print[ c ], {n, 1, 50} ]

%Y Cf. A055683.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 22 2000