3 × 72 × 29 × 281
1, 3, 7, 21, 29, 49, 87, 147, 203, 281, 609, 843, 1421, 1967, 4263, 5901, 8149, 13769, 24447, 41307, 57043, 171129, 399301 and 1197903
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.