34 × 127 × 137
1, 3, 9, 27, 81, 127, 137, 381, 411, 1143, 1233, 3429, 3699, 10287, 11097, 17399, 52197, 156591, 469773 and 1409319
No.
Its nearest Fibonacci number neighbors are 1346269 and 2178309.