3 × 7 × 11 × 31 × 151
1, 3, 7, 11, 21, 31, 33, 77, 93, 151, 217, 231, 341, 453, 651, 1023, 1057, 1661, 2387, 3171, 4681, 4983, 7161, 11627, 14043, 32767, 34881, 51491, 98301, 154473, 360437 and 1081311
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.