22 × 3 × 11 × 167
1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132, 167, 334, 501, 668, 1002, 1837, 2004, 3674, 5511, 7348, 11022 and 22044
No.
Its nearest Fibonacci number neighbors are 17711 and 28657.