52 × 11 × 151 × 3001
1, 5, 11, 25, 55, 151, 275, 755, 1661, 3001, 3775, 8305, 15005, 33011, 41525, 75025, 165055, 453151, 825275, 2265755, 4984661, 11328775, 24923305 and 124616525
No.
Its nearest Fibonacci number neighbors are 102334155 and 165580141.