52 × 11 × 31 × 41
1, 5, 11, 25, 31, 41, 55, 155, 205, 275, 341, 451, 775, 1025, 1271, 1705, 2255, 6355, 8525, 11275, 13981, 31775, 69905 and 349525
No.
Its nearest Fibonacci number neighbors are 317811 and 514229.