3 × 73 × 11 × 73
1, 3, 7, 11, 21, 33, 49, 73, 77, 147, 219, 231, 343, 511, 539, 803, 1029, 1533, 1617, 2409, 3577, 3773, 5621, 10731, 11319, 16863, 25039, 39347, 75117, 118041, 275429 and 826287
No.
Its nearest Fibonacci number neighbors are 514229 and 832040.