a(n) = gcd(1 + Fibonacci(n+1), 1 + Fibonacci(n)).

Terms

a(0) =1a(1) =2a(2) =1a(3) =1a(4) =2a(5) =3a(6) =1a(7) =2a(8) =1a(9) =7a(10) =2a(11) =5a(12) =1a(13) =18a(14) =1a(15) =13a(16) =2a(17) =47a(18) =1a(19) =34a(20) =1a(21) =123a(22) =2a(23) =89a(24) =1a(25) =322a(26) =1a(27) =233a(28) =2a(29) =843