A371598 a(n) = (Product_{i=1..n} Fibonacci(i)) mod Fibonacci(n + 1).

0, 1, 2, 1, 6, 6, 12, 2, 15, 16, 0, 49, 299, 220, 882, 252, 2176, 166, 495, 5720, 5251, 6065, 28224, 41650, 106947, 113288, 256737, 173841, 26840, 25379, 444150, 347278, 1834953, 8709610, 4046544, 2653673, 31127545, 47532000, 50717205, 147239197, 97769672, 37543458

Offset: 1

Author

Adnan Baysal, Mar 29 2024

Keywords

• nonn

Examples

			a(1) = 0 since A000045(1) = A000045(2) = 1 and 1 mod 1 = 0.
a(2) = (1 * 1) mod 2 = 1.
a(3) = (1 * 1 * 2) mod 3 = 2.
a(4) = (1 * 1 * 2 * 3) mod 5 = 1.
		

Crossrefs

Cf. A000045, A003266, A062347, A333599.

Programs

Mathematica

a[n_] := Mod[Fibonorial[n], Fibonacci[n + 1]]; Array[a, 50] (* Amiram Eldar, Mar 29 2024 *)

PARI

a(n) = my(f=fibonacci(n+1)); lift(prod(k=1, n, Mod(fibonacci(k), f))); \\ Michel Marcus, Apr 03 2024

Python

from sympy import fibonacci
def a(n):
    a_n = 1
    mod = fibonacci(n + 1)
    for i in range(1, n + 1):
        a_n = (a_n * fibonacci(i)) % mod
    return a_n

Formula

a(n) = A003266(n) mod A000045(n+1).