2 × 52 × 7 × 509
1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350, 509, 1018, 2545, 3563, 5090, 7126, 12725, 17815, 25450, 35630, 89075 and 178150
No.
Its nearest Fibonacci number neighbors are 121393 and 196418.