3 × 72 × 43 × 337
1, 3, 7, 21, 43, 49, 129, 147, 301, 337, 903, 1011, 2107, 2359, 6321, 7077, 14491, 16513, 43473, 49539, 101437, 304311, 710059 and 2130177
No.
Its nearest Fibonacci number neighbors are 1346269 and 2178309.