3 × 72 × 13 × 29
1, 3, 7, 13, 21, 29, 39, 49, 87, 91, 147, 203, 273, 377, 609, 637, 1131, 1421, 1911, 2639, 4263, 7917, 18473 and 55419
No.
Its nearest Fibonacci number neighbors are 46368 and 75025.