a(n) is the least i such that gcd(Fibonacci(i), i+x) > 1 for all x=0..n.

Terms

a(0) =5a(1) =10a(2) =18a(3) =30a(4) =30a(5) =30a(6) =30a(7) =180a(8) =180a(9) =180a(10) =180a(11) =840a(12) =840a(13) =1260a(14) =1260a(15) =1260a(16) =1260a(17) =24480a(18) =24480a(19) =63000a(20) =63000a(21) =63000a(22) =63000a(23) =63000a(24) =63000a(25) =63000a(26) =63000a(27) =63000a(28) =63000a(29) =356400