A037018 Conjecturally, largest k with no prime in [ k, k(1+1/n) ].

1, 8, 8, 24, 24, 32, 32, 114, 115, 116, 117, 117, 118, 119, 140, 140, 141, 200, 212, 212, 213, 294, 294, 318, 318, 319, 319, 319, 320, 524, 524, 525, 525, 525, 526, 526, 527, 527, 527, 1328, 1329, 1330, 1330, 1331, 1332, 1332, 1333, 1333, 1334, 1334, 1335