3 × 7 × 13 × 67 × 107
1, 3, 7, 13, 21, 39, 67, 91, 107, 201, 273, 321, 469, 749, 871, 1391, 1407, 2247, 2613, 4173, 6097, 7169, 9737, 18291, 21507, 29211, 50183, 93197, 150549, 279591, 652379 and 1957137
No.
Its nearest Fibonacci number neighbors are 1346269 and 2178309.