22 × 73 × 101 × 137
1, 2, 4, 73, 101, 137, 146, 202, 274, 292, 404, 548, 7373, 10001, 13837, 14746, 20002, 27674, 29492, 40004, 55348, 1010101, 2020202 and 4040404
No.
Its nearest Fibonacci number neighbors are 3524578 and 5702887.