22 × 3 × 7 × 43
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 43, 84, 86, 129, 172, 258, 301, 516, 602, 903, 1204, 1806 and 3612
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.