3 × 5 × 41 × 271 × 9091
1, 3, 5, 15, 41, 123, 205, 271, 615, 813, 1355, 4065, 9091, 11111, 27273, 33333, 45455, 55555, 136365, 166665, 372731, 1118193, 1863655, 2463661, 5590965, 7390983, 12318305, 36954915, 101010101, 303030303, 505050505 and 1515151515
No.
Its nearest Fibonacci number neighbors are 1134903170 and 1836311903.