5 × 13 × 29 × 71 × 911
1, 5, 13, 29, 65, 71, 145, 355, 377, 911, 923, 1885, 2059, 4555, 4615, 10295, 11843, 26419, 26767, 59215, 64681, 132095, 133835, 323405, 343447, 840853, 1717235, 1875749, 4204265, 9378745, 24384737 and 121923685
No.
Its nearest Fibonacci number neighbors are 102334155 and 165580141.