Least prime p such that the interval to the next prime contains n prime factors (counted multiply).
3, 11, 59, 71, 239, 7, 13, 103, 97, 79, 127, 73, 23, 31, 61, 157, 373, 383, 251, 89, 359, 401, 683, 701, 139, 337, 283, 241, 211, 631, 1471, 199, 1399, 661, 113, 619, 1511, 509, 293, 953, 317, 773, 1583, 863, 2423, 1831, 2251, 1933, 1381, 4057, 2803, 523, 1069
2
The interval between primes 3 and 5 contains 2 prime factors (2,2). The interval between primes 11 and 13 contains 3 prime factors (2,2,3).
T. D. Noe, Plot of 499 terms
T. D. Noe, Table of 499 terms
Eric W. Weisstein, MathWorld: Primes Gaps
(Mma) nn = 10000; t = Join[{0}, Table[Total[Transpose[FactorInteger[n]][[2]]], {n, 2, Prime[nn]}]]; t2 = Table[Total[t[[Range[Prime[n] + 1, Prime[n + 1] - 1]]]], {n, nn - 1}]; t3 = Sort[t2]; missing = Complement[Range[t3[[-1]]], t3][[2]]; Table[Prime[Position[t2, n, 1, 1][[1, 1]]], {n, 2, missing - 1}]
Cf. S000565.
nonn
T. D. Noe, Apr 08 2015