22 × 3 × 7 × 59
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 59, 84, 118, 177, 236, 354, 413, 708, 826, 1239, 1652, 2478 and 4956
No.
Its nearest Fibonacci number neighbors are 4181 and 6765.