Distance squared to the center of a “real" 4-lion from the origin.
10, 650, 2250, 15300, 15650, 19400, 34850, 68000, 96200, 101700, 108200, 112250, 115400, 139250, 144500, 178100, 198050, 222500, 243450, 262100, 265250, 266850, 270800, 324000, 365300, 372500, 375050, 378650, 411650, 434250, 441650, 449600, 463250, 477200, 479300
1
This is S000416 without the lions on the line x=y. Renze et al. discuss this on page 171 of the paper sited below.
T. D. Noe, Plot of 1561 pairs
T. D. Noe, Table of 1561 pairs
John Renze, Stan Wagon, and Brian Wick, The Gaussian Zoo, Experimental Math. 10:2, p. 161-173.
(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]; Union[Transpose[t][[1]]]
Cf. S000416.
nonn
T. D. Noe, Dec 19 2014