5 × 17 × 257 × 65537
1, 5, 17, 85, 257, 1285, 4369, 21845, 65537, 327685, 1114129, 5570645, 16843009, 84215045, 286331153 and 1431655765
No.
Its nearest Fibonacci number neighbors are 1134903170 and 1836311903.