5 × 11 × 271 × 9091
1, 5, 11, 55, 271, 1355, 2981, 9091, 14905, 45455, 100001, 500005, 2463661, 12318305, 27100271 and 135501355
No.
Its nearest Fibonacci number neighbors are 102334155 and 165580141.