32 × 5 × 11 × 23
1, 3, 5, 9, 11, 15, 23, 33, 45, 55, 69, 99, 115, 165, 207, 253, 345, 495, 759, 1035, 1265, 2277, 3795 and 11385
No.
Its nearest Fibonacci number neighbors are 10946 and 17711.