3 × 7 × 13 × 29 × 281
1, 3, 7, 13, 21, 29, 39, 87, 91, 203, 273, 281, 377, 609, 843, 1131, 1967, 2639, 3653, 5901, 7917, 8149, 10959, 24447, 25571, 57043, 76713, 105937, 171129, 317811, 741559 and 2224677
No.
Its nearest Fibonacci number neighbors are 2178309 and 3524578.