26 × 5 × 11
1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 64, 80, 88, 110, 160, 176, 220, 320, 352, 440, 704, 880, 1760 and 3520
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.