32 × 43 × 127 × 337
1, 3, 9, 43, 127, 129, 337, 381, 387, 1011, 1143, 3033, 5461, 14491, 16383, 42799, 43473, 49149, 128397, 130419, 385191, 1840357, 5521071 and 16563213
No.
Its nearest Fibonacci number neighbors are 14930352 and 24157817.