32 × 72 × 43 × 127
1, 3, 7, 9, 21, 43, 49, 63, 127, 129, 147, 301, 381, 387, 441, 889, 903, 1143, 2107, 2667, 2709, 5461, 6223, 6321, 8001, 16383, 18669, 18963, 38227, 49149, 56007, 114681, 267589, 344043, 802767 and 2408301
No.
Its nearest Fibonacci number neighbors are 2178309 and 3524578.