34 × 5 × 7 × 277
1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 81, 105, 135, 189, 277, 315, 405, 567, 831, 945, 1385, 1939, 2493, 2835, 4155, 5817, 7479, 9695, 12465, 17451, 22437, 29085, 37395, 52353, 87255, 112185, 157059, 261765 and 785295
No.
Its nearest Fibonacci number neighbors are 514229 and 832040.