2 × 3 × 11 × 17 × 19
1, 2, 3, 6, 11, 17, 19, 22, 33, 34, 38, 51, 57, 66, 102, 114, 187, 209, 323, 374, 418, 561, 627, 646, 969, 1122, 1254, 1938, 3553, 7106, 10659 and 21318
No.
Its nearest Fibonacci number neighbors are 17711 and 28657.