3 × 11 × 41 × 271 × 9091
1, 3, 11, 33, 41, 123, 271, 451, 813, 1353, 2981, 8943, 9091, 11111, 27273, 33333, 100001, 122221, 300003, 366663, 372731, 1118193, 2463661, 4100041, 7390983, 12300123, 27100271, 81300813, 101010101, 303030303, 1111111111 and 3333333333
No.
Its nearest Fibonacci number neighbors are 2971215073 and 4807526976.