22 × 3 × 11 × 97
1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 97, 132, 194, 291, 388, 582, 1067, 1164, 2134, 3201, 4268, 6402 and 12804
No.
Its nearest Fibonacci number neighbors are 10946 and 17711.