Gaussian primes strictly in the first quadrant, sorted by magnitude and imaginary part.

1, 1, 2, 1, 1, 2, 3, 2, 2, 3, 4, 1, 1, 4, 5, 2, 2, 5, 6, 1, 1, 6, 5, 4, 4, 5, 7, 2, 2, 7, 6, 5, 5, 6, 8, 3, 3, 8, 8, 5, 5, 8, 9, 4, 4, 9, 10, 1, 1, 10, 10, 3, 3, 10, 8, 7, 7, 8, 11, 4, 4, 11, 10, 7, 7, 10, 11, 6, 6, 11, 13, 2, 2, 13, 10, 9, 9, 10, 12, 7, 7, 12

1

This sequence is S000410 with the real and imaginary parts exchanged. However, the plot of the points in the complex plane is the same.

T. D. Noe, Plot of 1219 pairs

T. D. Noe, Table of 1219 pairs

Eric W. Weisstein, MathWorld: Gaussian Prime

(Mma) nn = 10; t = Select[Flatten[Table[a + b*I, {a, nn}, {b, nn}]], Abs[#] <= nn && PrimeQ[#, GaussianIntegers -> True] &]; t2 = Sort[t, Abs[#1] <= Abs[#2] &]; Flatten[Transpose[{Im /@ t2, Re /@ t2}]]

nonn

T. D. Noe, Dec 15 2014