3 × 7 × 11 × 13 × 9901
1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003, 9901, 29703, 69307, 108911, 128713, 207921, 326733, 386139, 762377, 900991, 1415843, 2287131, 2702973, 4247529, 9910901 and 29732703
No.
Its nearest Fibonacci number neighbors are 24157817 and 39088169.