32 × 7 × 11 × 13
1, 3, 7, 9, 11, 13, 21, 33, 39, 63, 77, 91, 99, 117, 143, 231, 273, 429, 693, 819, 1001, 1287, 3003 and 9009
No.
Its nearest Fibonacci number neighbors are 6765 and 10946.