3 × 7 × 11 × 151 × 331
1, 3, 7, 11, 21, 33, 77, 151, 231, 331, 453, 993, 1057, 1661, 2317, 3171, 3641, 4983, 6951, 10923, 11627, 25487, 34881, 49981, 76461, 149943, 349867, 549791, 1049601, 1649373, 3848537 and 11545611
No.
Its nearest Fibonacci number neighbors are 9227465 and 14930352.