Number of primes in the range n^2 to (n + log(n)/2)^2.

0, 1, 1, 2, 2, 4, 3, 4, 4, 5, 4, 6, 7, 7, 8, 8, 7, 8, 9, 11, 11, 9, 11, 14, 12, 13, 12, 14, 14, 14, 18, 17, 16, 16, 17, 15, 20, 22, 22, 21, 19, 19, 22, 22, 21, 22, 27, 25, 21, 26, 31, 28, 25, 24, 23, 29, 30, 29, 32, 30, 30, 33, 31, 32, 32, 30, 32, 32, 35, 38, 32

1

Dudek et al. mention something similar to this in section 4 of their paper.

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

Adrian Dudek, Loïc Grenié, and Giuseppe Molteni, Primes in explicit short intervals on RH, arXiv 1503.05403 (Feb 24 2015)

(Mma) Table[PrimePi[(n + Log[n]/2)^2] - PrimePi[n^2], {n, 100}]

Cf. A014085.

nonn

T. D. Noe, Mar 20 2015