A024835 a(n) = least m such that if r and s in {1/2, 1/4, 1/6, ..., 1/2n} satisfy r > s, then r > k/m > (k-1)/m > s for some integer k.

7, 17, 31, 49, 81, 111, 157, 197, 257, 307, 381, 441, 529, 625, 703, 813, 931, 1025, 1157, 1297, 1407, 1561, 1723, 1849, 2025, 2209, 2401, 2551, 2757, 2971, 3193, 3365, 3601, 3845, 4097, 4291, 4557, 4831, 5113, 5329, 5625, 5929, 6241, 6561, 6807, 7141, 7483, 7833