23 × 3 × 7 × 17
1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 24, 28, 34, 42, 51, 56, 68, 84, 102, 119, 136, 168, 204, 238, 357, 408, 476, 714, 952, 1428 and 2856
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.