214 × 7
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1024, 1792, 2048, 3584, 4096, 7168, 8192, 14336, 16384, 28672, 57344 and 114688
No.
Its nearest Fibonacci number neighbors are 75025 and 121393.