%I #20 Dec 09 2024 19:46:39

%S 1,3,8,48,144,329,2584,15456,104005,832040,1866294,34111385,267914296,

%T 1602508992,10783446409,193501094490,1548008755920,3472236254411,

%U 166151337293088,498454011879264,1118049290473933,53500214605455696,360008399296352015,2460986135945634432

%N Multiplicative inverse of Fibonacci(prime(n)) modulo Fibonacci(prime(n+1)).

%C Since Fibonacci numbers have the property that gcd(x,y) = gcd(Fibonacci(x), Fibonacci(y)), the modular inverse will always exist for this sequence.

%F a(n) = invmod(Fibonacci(prime(n)), Fibonacci(prime(n+1))).

%p a:= n-> (f-> (1/f(n) mod f(n+1)))(j->combinat[fibonacci](ithprime(j))):

%p seq(a(n), n=1..25); # _Alois P. Heinz_, Aug 12 2019

%t Table[ModularInverse[Fibonacci[Prime[n]], Fibonacci[Prime[n+1]]], {n, 20}]

%o (PARI) a(n)={lift(1/(Mod(fibonacci(prime(n)), fibonacci(prime(n+1)))))} \\ _Andrew Howroyd_, Aug 12 2019

%Y Cf. A000045, A030426, A069830.

%K nonn

%O 1,2

%A _Dragos Ristache_, Aug 08 2019