3 × 7 × 11 × 37 × 101
1, 3, 7, 11, 21, 33, 37, 77, 101, 111, 231, 259, 303, 407, 707, 777, 1111, 1221, 2121, 2849, 3333, 3737, 7777, 8547, 11211, 23331, 26159, 41107, 78477, 123321, 287749 and 863247
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.