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%I #3 May 03 2013 18:57:50
%S 0,3,4,5,4,7,6,8,8,9,6,9,16,8,12,11,8,18,16,12,18,15,14,15,10,14,18,
%T 28,16,19,22,14,34,23,20,19,22,18,16,27,18,31,40,22,28,26,16,36,28,20,
%U 36,33,20,35,32,26,40,40,26,28,34,24,46,37,28,45,30,34,36
%N Number of first-quadrant Gaussian primes at taxicab distance 2n-1 from the origin.
%C Except for 1+I, 1-I, -1+I, and -1-I, all Gaussian primes are an odd taxicab distance from the origin. Primes on the x- and y-axis are counted only once. That is, although p and p*I are Gaussian primes (for primes p in A002145), we count only p as being a first-quadrant Gaussian prime.
%H T. D. Noe, <a href="/A225072/b225072.txt">Table of n, a(n) for n = 1..10000</a>
%t Table[cnt = 0; Do[If[PrimeQ[n - i + I*i, GaussianIntegers -> True], cnt++], {i, 0, n}]; Do[If[PrimeQ[i - n + I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 0, -1}]; Do[If[PrimeQ[i - n - I*i, GaussianIntegers -> True], cnt++], {i, 1, n}]; Do[If[PrimeQ[n - i - I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 1, -1}]; cnt, {n, 1, 200, 2}]/4
%Y Cf. A002145, A218858, A225071.
%K nonn
%O 1,2
%A _T. D. Noe_, May 03 2013
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