22 × 5 × 13 × 23
1, 2, 4, 5, 10, 13, 20, 23, 26, 46, 52, 65, 92, 115, 130, 230, 260, 299, 460, 598, 1196, 1495, 2990 and 5980
No.
Its nearest Fibonacci number neighbors are 4181 and 6765.