33 × 29 × 151 × 557
1, 3, 9, 27, 29, 87, 151, 261, 453, 557, 783, 1359, 1671, 4077, 4379, 5013, 13137, 15039, 16153, 39411, 48459, 84107, 118233, 145377, 252321, 436131, 756963, 2270889, 2439103, 7317309, 21951927 and 65855781
No.
Its nearest Fibonacci number neighbors are 63245986 and 102334155.