3 × 5 × 11 × 23 × 101
1, 3, 5, 11, 15, 23, 33, 55, 69, 101, 115, 165, 253, 303, 345, 505, 759, 1111, 1265, 1515, 2323, 3333, 3795, 5555, 6969, 11615, 16665, 25553, 34845, 76659, 127765 and 383295
No.
Its nearest Fibonacci number neighbors are 317811 and 514229.