213 × 13
1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 256, 416, 512, 832, 1024, 1664, 2048, 3328, 4096, 6656, 8192, 13312, 26624, 53248 and 106496
No.
Its nearest Fibonacci number neighbors are 75025 and 121393.