5 × 11 × 17 × 23 × 73
1, 5, 11, 17, 23, 55, 73, 85, 115, 187, 253, 365, 391, 803, 935, 1241, 1265, 1679, 1955, 4015, 4301, 6205, 8395, 13651, 18469, 21505, 28543, 68255, 92345, 142715, 313973 and 1569865
No.
Its nearest Fibonacci number neighbors are 1346269 and 2178309.