32 × 11 × 151 × 331
1, 3, 9, 11, 33, 99, 151, 331, 453, 993, 1359, 1661, 2979, 3641, 4983, 10923, 14949, 32769, 49981, 149943, 449829, 549791, 1649373 and 4948119
No.
Its nearest Fibonacci number neighbors are 3524578 and 5702887.