A262776 a(n) = Fibonacci(n!) mod Fibonacci(n)!.

0, 0, 0, 0, 0, 0, 20160, 1098377280, 10712200669548618240, 157910199555786679826546221836620444160, 12162675222629942931022379230724715707339402614012620710827200735689241600

Offset

0,7

Comments

Inspired by A261626.

Is there a possibility of observing that a(n) = 0 for n > 5?

Links

Alois P. Heinz, Table of n, a(n) for n = 0..14

Formula

a(n) = A063374(n) mod A060001(n), for n > 0.

Example

a(0) = Fibonacci(0!) mod Fibonacci(0)! = 1 mod 1 = 0.
a(1) = Fibonacci(1!) mod Fibonacci(1)! = 1 mod 1 = 0.
a(2) = Fibonacci(2!) mod Fibonacci(2)! = 1 mod 1 = 0.
a(3) = Fibonacci(3!) mod Fibonacci(3)! = 8 mod 2 = 0.
a(4) = Fibonacci(4!) mod Fibonacci(4)! = 46368 mod 6 = 0.

Mathematica

Table[Mod[Fibonacci[n!], Fibonacci[n]!], {n, 0, 9}] (* Michael De Vlieger, Oct 01 2015 *)

Prog

(PARI) a(n) = fibonacci(n!) % fibonacci(n)!;
vector(10, n, a(n-1))
(Magma) [Fibonacci(Factorial(n)) mod Factorial(Fibonacci(n)): n in [0..10]]; // Vincenzo Librandi, Oct 01 2015
(Python)
from gmpy2 import fac, fib
def A262776(n):
    if n < 2:
        return 0
    a, b, m = 0, 1, fac(fib(n))
    for i in range(fac(n)-1):
        b, a = (b+a) % m, b
    return int(b) # Chai Wah Wu, Oct 03 2015

Crossrefs

Cf. A000045, A060001, A063374, A261626.

Sequence in context: A003801 A305186 A181233 * A119648 A127224 A235523

Adjacent sequences: A262773 A262774 A262775 * A262777 A262778 A262779

Keyword

nonn,easy

Author

Altug Alkan, Oct 01 2015

Extensions

a(10) from Alois P. Heinz, Oct 01 2015

Status

approved