A309578 Multiplicative inverse of Fibonacci(prime(n)) modulo Fibonacci(prime(n+1)).

1, 3, 8, 48, 144, 329, 2584, 15456, 104005, 832040, 1866294, 34111385, 267914296, 1602508992, 10783446409, 193501094490, 1548008755920, 3472236254411, 166151337293088, 498454011879264, 1118049290473933, 53500214605455696, 360008399296352015, 2460986135945634432

Offset: 1

Author

Dragos Ristache, Aug 08 2019

Keywords

• nonn

Comments

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

Crossrefs

Cf. A000045, A030426, A069830.

Programs

Maple

a:= n-> (f-> (1/f(n) mod f(n+1)))(j->combinat[fibonacci](ithprime(j))):
seq(a(n), n=1..25);  # Alois P. Heinz, Aug 12 2019

Mathematica

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

PARI

a(n)={lift(1/(Mod(fibonacci(prime(n)), fibonacci(prime(n+1)))))} \\ Andrew Howroyd, Aug 12 2019

Formula

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