52 × 7 × 13 × 509
1, 5, 7, 13, 25, 35, 65, 91, 175, 325, 455, 509, 2275, 2545, 3563, 6617, 12725, 17815, 33085, 46319, 89075, 165425, 231595 and 1157975
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.