2 × 3 × 7 × 11 × 73
1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 73, 77, 146, 154, 219, 231, 438, 462, 511, 803, 1022, 1533, 1606, 2409, 3066, 4818, 5621, 11242, 16863 and 33726
No.
Its nearest Fibonacci number neighbors are 28657 and 46368.