35 × 127 × 137
1, 3, 9, 27, 81, 127, 137, 243, 381, 411, 1143, 1233, 3429, 3699, 10287, 11097, 17399, 30861, 33291, 52197, 156591, 469773, 1409319 and 4227957
No.
Its nearest Fibonacci number neighbors are 3524578 and 5702887.