3 × 7 × 11 × 13 × 101
1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 101, 143, 231, 273, 303, 429, 707, 1001, 1111, 1313, 2121, 3003, 3333, 3939, 7777, 9191, 14443, 23331, 27573, 43329, 101101 and 303303
No.
Its nearest Fibonacci number neighbors are 196418 and 317811.