33 × 11 × 23 × 101
1, 3, 9, 11, 23, 27, 33, 69, 99, 101, 207, 253, 297, 303, 621, 759, 909, 1111, 2277, 2323, 2727, 3333, 6831, 6969, 9999, 20907, 25553, 29997, 62721, 76659, 229977 and 689931
No.
Its nearest Fibonacci number neighbors are 514229 and 832040.