5 × 11 × 13 × 29 × 71
1, 5, 11, 13, 29, 55, 65, 71, 143, 145, 319, 355, 377, 715, 781, 923, 1595, 1885, 2059, 3905, 4147, 4615, 10153, 10295, 20735, 22649, 26767, 50765, 113245, 133835, 294437 and 1472185
No.
Its nearest Fibonacci number neighbors are 1346269 and 2178309.