24 × 7 × 1201
1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 1201, 2402, 4804, 8407, 9608, 16814, 19216, 33628, 67256 and 134512
No.
Its nearest Fibonacci number neighbors are 121393 and 196418.