3 × 5 × 7 × 11 × 41
1, 3, 5, 7, 11, 15, 21, 33, 35, 41, 55, 77, 105, 123, 165, 205, 231, 287, 385, 451, 615, 861, 1155, 1353, 1435, 2255, 3157, 4305, 6765, 9471, 15785 and 47355
No.
Its nearest Fibonacci number neighbors are 46368 and 75025.