3 × 7 × 13 × 37 × 101
1, 3, 7, 13, 21, 37, 39, 91, 101, 111, 259, 273, 303, 481, 707, 777, 1313, 1443, 2121, 3367, 3737, 3939, 9191, 10101, 11211, 26159, 27573, 48581, 78477, 145743, 340067 and 1020201
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.