3 × 72 × 11 × 181
1, 3, 7, 11, 21, 33, 49, 77, 147, 181, 231, 539, 543, 1267, 1617, 1991, 3801, 5973, 8869, 13937, 26607, 41811, 97559 and 292677
No.
Its nearest Fibonacci number neighbors are 196418 and 317811.