2 × 3 × 11 × 13 × 29
1, 2, 3, 6, 11, 13, 22, 26, 29, 33, 39, 58, 66, 78, 87, 143, 174, 286, 319, 377, 429, 638, 754, 858, 957, 1131, 1914, 2262, 4147, 8294, 12441 and 24882
No.
Its nearest Fibonacci number neighbors are 17711 and 28657.