32 × 11 × 23 × 101
1, 3, 9, 11, 23, 33, 69, 99, 101, 207, 253, 303, 759, 909, 1111, 2277, 2323, 3333, 6969, 9999, 20907, 25553, 76659 and 229977
No.
Its nearest Fibonacci number neighbors are 196418 and 317811.