2 × 3 × 11 × 23 × 29
1, 2, 3, 6, 11, 22, 23, 29, 33, 46, 58, 66, 69, 87, 138, 174, 253, 319, 506, 638, 667, 759, 957, 1334, 1518, 1914, 2001, 4002, 7337, 14674, 22011 and 44022
No.
Its nearest Fibonacci number neighbors are 28657 and 46368.