32 × 7 × 31 × 151
1, 3, 7, 9, 21, 31, 63, 93, 151, 217, 279, 453, 651, 1057, 1359, 1953, 3171, 4681, 9513, 14043, 32767, 42129, 98301 and 294903
No.
Its nearest Fibonacci number neighbors are 196418 and 317811.