3 × 7 × 112 × 13
1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 121, 143, 231, 273, 363, 429, 847, 1001, 1573, 2541, 3003, 4719, 11011 and 33033
No.
Its nearest Fibonacci number neighbors are 28657 and 46368.