5 × 13 × 29 × 141961
1, 5, 13, 29, 65, 145, 377, 1885, 141961, 709805, 1845493, 4116869, 9227465, 20584345, 53519297 and 267596485
No.
Its nearest Fibonacci number neighbors are 165580141 and 267914296.