7 × 11 × 31 × 151 × 331
1, 7, 11, 31, 77, 151, 217, 331, 341, 1057, 1661, 2317, 2387, 3641, 4681, 10261, 11627, 25487, 32767, 49981, 51491, 71827, 112871, 349867, 360437, 549791, 790097, 1549411, 3848537, 10845877, 17043521 and 119304647
No.
Its nearest Fibonacci number neighbors are 102334155 and 165580141.