A085077 Fibonacci number with a prime signature that has not occurred earlier.

1, 2, 8, 21, 144, 610, 2584, 6765, 46368, 75025, 832040, 14930352, 102334155, 701408733, 4807526976, 12586269025, 86267571272, 225851433717, 1548008755920, 190392490709135, 498454011879264, 23416728348467685