211 × 13
1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 256, 416, 512, 832, 1024, 1664, 2048, 3328, 6656, 13312 and 26624
No.
Its nearest Fibonacci number neighbors are 17711 and 28657.