The squared distance between adjacent points of S000921.
1, 2, 4, 4, 2, 2, 4, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4, 4, 4, 2, 2, 8, 2, 10, 4, 10, 4, 8, 4, 4, 8, 4, 16, 10, 2, 10, 2, 4, 2, 2, 20, 4, 2, 4, 10, 4, 16, 2, 4, 4, 18, 4, 4, 8, 16, 4, 2, 4, 10, 2, 2, 16, 4, 20, 20, 4, 10, 4, 2, 4, 8, 10, 10, 8, 4, 2, 10, 8, 4, 10, 2, 4
1
Note that the terms of this sequence appear in A128106.
T. D. Noe, Plot of 2000 terms
T. D. Noe, Table of 2000 terms
(Mma) nn = 10; pts = 1000; d = Sort[Select[Flatten[Table[{Sqrt[i^2 + j^2], i, j}, {i, 0, nn}, {j, 0, nn}], 1], #[[1]] <= nn &], #1[[1]] < #2[[1]] &]; p = 1 + I; t = {p}; Do[i = 2; While[i <= Length[d] && ! PrimeQ[p + d[[i, 2]] + I*d[[i, 3]], GaussianIntegers -> True], i++]; If[i >= Length[d], Return[], p = p + d[[i, 2]] + I*d[[i, 3]]; AppendTo[t, p]], {pts - 1}]; Abs[Differences[t]]^2
Cf. A128106, S000921, S000922.
nonn
T. D. Noe, Jul 25 2016