## S000417

Position of the center of a 4-lion in the first quadrant, sorted by magnitude and real part.

2, 2, 1, 3, 3, 1, 5, 5, 5, 25, 25, 5, 25, 25, 30, 30, 15, 45, 45, 15, 35, 35, 70, 70, 85, 85, 30, 120, 120, 30, 5, 125, 125, 5, 50, 130, 130, 50, 100, 100, 110, 110, 65, 175, 175, 65, 20, 260, 260, 20, 10, 310, 310, 10, 225, 225, 210, 240, 240, 210, 230, 230

1

The smallest lion is a collection of four Gaussian primes z-1, z+1, z-i, and z+i for a complex number z. Sequence S000416 lists the distance from the origin to the center of a 4-lion. The 4th link below shows a plot exhibiting the symmetry. The terms on the diagonal x=y have coordinates x given in A109306.

T. D. Noe, Plot of 3252 pairs

T. D. Noe, Table of 3252 pairs

David Bessoud and Stan Wagon, A Course in Computational Number Theory, Key College Publishing, 2000.

T. D. Noe, Numbers plotted in the complex plane

Eric W. Weisstein, MathWorld: Gaussian Prime

(Mma) nn = 1000; t = {}; Do[z = x + I*y; If[PrimeQ[z - 1, GaussianIntegers -> True] && PrimeQ[z + 1, GaussianIntegers -> True] && PrimeQ[z - I, GaussianIntegers -> True] && PrimeQ[z + I, GaussianIntegers -> True], If[Abs[z] <= nn, t = AppendTo[t, {Abs[z]^2, {x, y}}]; If[x != y, AppendTo[t, {Abs[z]^2, {y, x}}]]]], {x, 0, nn}, {y, x}]; t = Sort[t]; Transpose[t][[2]]

Cf. A109306, S000416.

nonn

T. D. Noe, Dec 16 2014