34 × 29 × 557
1, 3, 9, 27, 29, 81, 87, 261, 557, 783, 1671, 2349, 5013, 15039, 16153, 45117, 48459, 145377, 436131 and 1308393
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.