3 × 31 × 37 × 2906161
1, 3, 31, 37, 93, 111, 1147, 3441, 2906161, 8718483, 90090991, 107527957, 270272973, 322583871, 3333366667 and 10000100001
No.
Its nearest Fibonacci number neighbors are 7778742049 and 12586269025.