3 × 52 × 11 × 31
1, 3, 5, 11, 15, 25, 31, 33, 55, 75, 93, 155, 165, 275, 341, 465, 775, 825, 1023, 1705, 2325, 5115, 8525 and 25575
No.
Its nearest Fibonacci number neighbors are 17711 and 28657.