5 × 7 × 11 × 23 × 73
1, 5, 7, 11, 23, 35, 55, 73, 77, 115, 161, 253, 365, 385, 511, 803, 805, 1265, 1679, 1771, 2555, 4015, 5621, 8395, 8855, 11753, 18469, 28105, 58765, 92345, 129283 and 646415
No.
Its nearest Fibonacci number neighbors are 514229 and 832040.