23 × 7 × 29 × 59
1, 2, 4, 7, 8, 14, 28, 29, 56, 58, 59, 116, 118, 203, 232, 236, 406, 413, 472, 812, 826, 1624, 1652, 1711, 3304, 3422, 6844, 11977, 13688, 23954, 47908 and 95816
No.
Its nearest Fibonacci number neighbors are 75025 and 121393.