## S000422

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

1, 3, 3, 1, 5, 25, 25, 5, 15, 45, 45, 15, 30, 120, 120, 30, 5, 125, 125, 5, 50, 130, 130, 50, 65, 175, 175, 65, 20, 260, 260, 20, 10, 310, 310, 10, 210, 240, 240, 210, 110, 310, 310, 110, 5, 335, 335, 5, 230, 250, 250, 230, 215, 305, 305, 215, 220, 310, 310

1

Sequence S000421 lists the distances of these points from the origin. At first, it appears that there are always two points at each distance. But this is proved false by points at distances 63574250 and 86359850.

T. D. Noe, Plot of 3126 terms

T. D. Noe, Table of 3126 terms

John Renze, Stan Wagon, and Brian Wick, The Gaussian Zoo, Experimental Math. 10:2, p. 161-173.

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

(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}}]; AppendTo[t, {Abs[z]^2, {y, x}}]]], {x, 0, nn}, {y, x-1}]; t = Sort[t]; Transpose[t][[2]]

Cf. S000421.

nonn

T. D. Noe, Dec 19 2014