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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Dragos Ristache

Dragos Ristache's wiki page.

Dragos Ristache has authored 1 sequences.

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

Original entry on oeis.org

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

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Author

Dragos Ristache, Aug 08 2019

Keywords

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))).

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