23 × 5 × 232
1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 529, 920, 1058, 2116, 2645, 4232, 5290, 10580 and 21160
No.
Its nearest Fibonacci number neighbors are 17711 and 28657.