3 × 7 × 337 × 5419
1, 3, 7, 21, 337, 1011, 2359, 5419, 7077, 16257, 37933, 113799, 1826203, 5478609, 12783421 and 38350263
No.
Its nearest Fibonacci number neighbors are 24157817 and 39088169.