32 × 7 × 127 × 337
1, 3, 7, 9, 21, 63, 127, 337, 381, 889, 1011, 1143, 2359, 2667, 3033, 7077, 8001, 21231, 42799, 128397, 299593, 385191, 898779 and 2696337
No.
Its nearest Fibonacci number neighbors are 2178309 and 3524578.