32 × 11 × 41 × 367
1, 3, 9, 11, 33, 41, 99, 123, 367, 369, 451, 1101, 1353, 3303, 4037, 4059, 12111, 15047, 36333, 45141, 135423, 165517, 496551 and 1489653
No.
Its nearest Fibonacci number neighbors are 1346269 and 2178309.