23 × 13 × 29 × 421
1, 2, 4, 8, 13, 26, 29, 52, 58, 104, 116, 232, 377, 421, 754, 842, 1508, 1684, 3016, 3368, 5473, 10946, 12209, 21892, 24418, 43784, 48836, 97672, 158717, 317434, 634868 and 1269736
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.