Maximum difference between primes less than e^n.

2, 4, 6, 14, 14, 20, 34, 34, 52, 72, 86, 112, 114, 148, 154, 210, 220, 222, 282

2

The paper by Maynard does not mention this sequence.

T. D. Noe, Plot of terms 2 to 20

James Maynard, Large gaps between primes, arXiv 1408.5110 (Aug 21 2014)

(Mma) Table[Max[Differences[Prime[Range[PrimePi[E^n]]]]], {n, 2, 15}]

Cf. A038460 (similar, but 10^n), S000209.

nonn

T. D. Noe, Aug 23 2014