32 × 31 × 41 × 271
1, 3, 9, 31, 41, 93, 123, 271, 279, 369, 813, 1271, 2439, 3813, 8401, 11111, 11439, 25203, 33333, 75609, 99999, 344441, 1033323 and 3099969
No.
Its nearest Fibonacci number neighbors are 2178309 and 3524578.