The record number of composite numbers around S000384(n)^2.
2, 4, 6, 14, 18, 20, 24, 26, 30, 34, 36, 40, 52, 54, 58, 66, 78, 82, 132, 150, 168, 180, 190, 200, 226, 252, 280, 288, 310, 324, 354
1
T. D. Noe, Plot of 31 terms
(Mma) t = {}; mx = 0; Do[k = n^2; k2 = PrimePi[k]; diff = Prime[k2 + 1] - Prime[k2]; If[diff > mx, mx = diff; AppendTo[t, {n, diff}]], {n, 2, 10000}]; Transpose[t][[2]]
Cf. A058043 (nextprime(n^2)-prevprime(n^2)), S000384.
nonn,hard
T. D. Noe, Nov 25 2014