3 × 72 × 13 × 37
1, 3, 7, 13, 21, 37, 39, 49, 91, 111, 147, 259, 273, 481, 637, 777, 1443, 1813, 1911, 3367, 5439, 10101, 23569 and 70707
No.
Its nearest Fibonacci number neighbors are 46368 and 75025.