2 × 52 × 7 × 13
1, 2, 5, 7, 10, 13, 14, 25, 26, 35, 50, 65, 70, 91, 130, 175, 182, 325, 350, 455, 650, 910, 2275 and 4550
No.
Its nearest Fibonacci number neighbors are 4181 and 6765.