22 × 3 × 11 × 3889
1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132, 3889, 7778, 11667, 15556, 23334, 42779, 46668, 85558, 128337, 171116, 256674 and 513348
No.
Its nearest Fibonacci number neighbors are 317811 and 514229.