Difference between the the least prime >= n and the greatest prime <= 2*n/3.

3, 3, 4, 4, 8, 6, 6, 6, 6, 6, 10, 10, 10, 10, 8, 8, 12, 10, 10, 10, 16, 16, 16, 12, 12, 12, 12, 12, 18, 18, 18, 18, 14, 14, 18, 18, 18, 18, 20, 20, 24, 18, 18, 18, 22, 22, 22, 22, 22, 22, 28, 28, 28, 22, 22, 22, 24, 24, 30, 26, 26, 26, 24, 24, 28, 28, 28, 28, 26

3

This differs from S000725 only at the terms for n = 10, 14, 15, 16, and 57.

T. D. Noe, Plot of 998 terms

T. D. Noe, Table of 998 terms

Wikipedia, Central binomial coefficient

(Mma) Table[Prime[PrimePi[n] + 1] - Prime[PrimePi[Floor[2 n/3]]], {n, 3, 100}]

Cf. S000725.

nonn

T. D. Noe, Oct 16 2015