3 × 31 × 37 × 41 × 271
1, 3, 31, 37, 41, 93, 111, 123, 271, 813, 1147, 1271, 1517, 3441, 3813, 4551, 8401, 10027, 11111, 25203, 30081, 33333, 47027, 141081, 310837, 344441, 411107, 932511, 1033323, 1233321, 12744317 and 38232951
No.
Its nearest Fibonacci number neighbors are 24157817 and 39088169.