211 × 11
1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 256, 352, 512, 704, 1024, 1408, 2048, 2816, 5632, 11264 and 22528
No.
Its nearest Fibonacci number neighbors are 17711 and 28657.