22 × 3 × 7 × 113
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 113, 226, 339, 452, 678, 791, 1356, 1582, 2373, 3164, 4746 and 9492
No.
Its nearest Fibonacci number neighbors are 6765 and 10946.