2 × 3 × 5 × 7 × 13
1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.