32 × 7 × 19 × 281
1, 3, 7, 9, 19, 21, 57, 63, 133, 171, 281, 399, 843, 1197, 1967, 2529, 5339, 5901, 16017, 17703, 37373, 48051, 112119 and 336357
No.
Its nearest Fibonacci number neighbors are 317811 and 514229.