3 × 7 × 31 × 151 × 331
1, 3, 7, 21, 31, 93, 151, 217, 331, 453, 651, 993, 1057, 2317, 3171, 4681, 6951, 10261, 14043, 30783, 32767, 49981, 71827, 98301, 149943, 215481, 349867, 1049601, 1549411, 4648233, 10845877 and 32537631
No.
Its nearest Fibonacci number neighbors are 24157817 and 39088169.