52 × 7 × 13 × 11981
1, 5, 7, 13, 25, 35, 65, 91, 175, 325, 455, 2275, 11981, 59905, 83867, 155753, 299525, 419335, 778765, 1090271, 2096675, 3893825, 5451355 and 27256775
No.
Its nearest Fibonacci number neighbors are 24157817 and 39088169.