The n 4-tuples of primes whose cubes sum to S001028(n).
2, 2, 2, 2, 5, 11, 13, 19, 7, 7, 17, 17, 13, 43, 47, 47, 19, 31, 47, 53, 29, 31, 31, 59, 17, 71, 73, 79, 23, 61, 67, 89, 37, 37, 83, 83, 43, 47, 53, 97, 23, 61, 137, 139, 23, 73, 107, 157, 43, 47, 113, 157, 47, 53, 97, 163, 53, 67, 73, 167, 5, 71, 181, 211
1
The n 4-tuples are sorted.
T. D. Noe, Plot of triange of 13 rows
T. D. Noe, Table of triangle of 13 rows
Example: the second row has the eight terms {5,11,13,19,7,7,17,17} for 10512 = 5^3 + 11^3 + 13^3 + 19^3 = 7^3 + 7^3 + 17^3 + 17^3.
(Mma) d = {32, 10512, 289350, 1244880, 5496120, 15681708, 7025200, 101965500, 94324230, 180710530}; Table[s = FindInstance[u^3 + x^3 + y^3 + z^3 == j && u > 0 && x > 0 && y > 0 && z > 0 && u <= x <= y <= z, {u, x, y, z}, Primes, 20]; Table[Flatten[s][[i, 2]], {i, 4*Length[s]}], {j, d}]
nonn,tabf
T. D. Noe, May 16 2017