Maximum difference between primes less than 2^n.

1, 2, 4, 6, 6, 14, 14, 14, 20, 34, 34, 34, 44, 72, 72, 72, 86, 114, 114, 148, 148, 154, 154, 210, 220, 222, 248, 282, 282

2

The paper by Maynard does not mention this sequence.

T. D. Noe, Plot of terms 2 to 30

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

(Mma) Table[Max[Differences[Prime[Range[PrimePi[2^n]]]]], {n, 2, 20}]

Cf. A038460 (similar, but 10^n), S000210.

nonn

T. D. Noe, Aug 23 2014