22 × 5 × 13 × 509
1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260, 509, 1018, 2036, 2545, 5090, 6617, 10180, 13234, 26468, 33085, 66170 and 132340
No.
Its nearest Fibonacci number neighbors are 121393 and 196418.