25 × 11 × 73
1, 2, 4, 8, 11, 16, 22, 32, 44, 73, 88, 146, 176, 292, 352, 584, 803, 1168, 1606, 2336, 3212, 6424, 12848 and 25696
No.
Its nearest Fibonacci number neighbors are 17711 and 28657.