32 × 7 × 43 × 337
1, 3, 7, 9, 21, 43, 63, 129, 301, 337, 387, 903, 1011, 2359, 2709, 3033, 7077, 14491, 21231, 43473, 101437, 130419, 304311 and 912933
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.