[seqfan] Iterative transform of integer sequence

[zak seidov]

 Iterative transform of A00040

 {{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89,...},
  {4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99,...},
  {5, 28, 32, 53, 58, 62, 74, 96, 136, 141, 147, 152, 157, 173, 178, 183, 189, 211, 221,...}, 
  {30, 60, 68, 85, 116, 144, 165, 186, 200, 216, 260, 270, 359, 399, 420, 426, 445, 482,...}, 
  {45, 64, 130, 193, 208, 238, 265, 379, 423, 492, 519, 561, 591, 674, 759, 771,...}, 
  {97, 223, 322, 401, 540, 576, 765, 816, 920, 994, 1031, 1384, 1422, 1475,...}, 
  {160, 558, 868, 957, 1403, 1531, 1598, 1680, 1761,...}, 
  {359, 713, 1180, 1467, 1639, 1808,...}, 
  {536,1553,4179,5178,6335,7865,9274,10665,13402,14644,15156,...},
  {2866,7100,14023,14900,15838,17837,20121,23987,26024,...},
  {4983,15369,18979,22054,...},
  {...}}

1st column: {2,4,5,30,45,97,160,359,536,2866,4983,...}
2nd column: {3,6,28,60,64,223,558,713,1553,7100,15369,...} 
Old hat? Interesting? Worth submitting?

Mathematica:  
NestList[Select[(Rest[#] + Most[#])/2, IntegerQ] &, 
Prime[Range[1000]], 10]