Numbers that are the sum of cubes of four primes.
32, 51, 70, 89, 108, 149, 168, 187, 206, 266, 285, 304, 367, 383, 386, 402, 405, 424, 484, 500, 503, 522, 601, 620, 702, 718, 721, 740, 819, 838, 936, 1037, 1056, 1154, 1355, 1372, 1374, 1393, 1412, 1472, 1491, 1510, 1589, 1608, 1690, 1706, 1709, 1728, 1807
1
It appears that sums increase linearly.
T. D. Noe, Plot of 10000 terms
T. D. Noe, Table of 10000 terms
Alessandro Languasco and Alessandro Zaccagnini, Sums of four prime cubes in short intervals, arXiv 1705.04457 (May 12 2017)
(Mma) nn = 10; Select[Union[Flatten[Table[Prime[i]^3 + Prime[j]^3 + Prime[k]^3 + Prime[l]^3, {i, nn}, {j, i, nn}, {k, j, nn}, {l, k, nn}]]], # <= Prime[nn]^3 + 3*Prime[1]^3 &]
nonn
T. D. Noe, May 16 2017