3 × 132 × 109 × 397
1, 3, 13, 39, 109, 169, 327, 397, 507, 1191, 1417, 4251, 5161, 15483, 18421, 43273, 55263, 67093, 129819, 201279, 562549, 1687647, 7313137 and 21939411
No.
Its nearest Fibonacci number neighbors are 14930352 and 24157817.