## S000416

Distance squared to the center of a 4-lion from the origin.

8, 10, 50, 650, 1250, 1800, 2250, 2450, 9800, 14450, 15300, 15650, 19400, 20000, 24200, 34850, 68000, 96200, 101250, 101700, 105800, 108200, 112250, 115400, 135200, 139250, 144500, 162450, 168200, 178100, 198050, 204800, 222500, 243450, 262100, 265250, 266850

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 S000417 lists the complex coordinates z of the center of 4-lions in the first quadrant. Each distance occurs only once in this list even though there are 2 first-quadrant lions if the lion is not on the diagonal.

T. D. Noe, Plot of 1687 terms

T. D. Noe, Table of 1687 terms

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

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]; Union[Transpose[t][[1]]]

Cf. S000417.

nonn

T. D. Noe, Dec 16 2014