3 × 41 × 271 × 9091
1, 3, 41, 123, 271, 813, 9091, 11111, 27273, 33333, 372731, 1118193, 2463661, 7390983, 101010101 and 303030303
No.
Its nearest Fibonacci number neighbors are 267914296 and 433494437.