A262398 a(n) = prime(n)! mod prime(n!).

0, 0, 3, 56, 511, 194, 46976, 104633, 546681, 41130177, 643108140, 7034542959, 65748733699, 1518781632657, 35097481516962, 396029533782911, 4146710666095789, 159899356955923308, 3662069108121609141, 109629928744379590001, 828180977946159463007

Offset: 1

Author

Altug Alkan, Sep 21 2015

Keywords

• nonn

Comments

Inspired by A261997.

a(n) = n and a(n) = prime(n-1) for n=3.

a(n) = 0 only for n=1 and n=2. What is the minimum value of a(n) for n > 2? Is there a possibility of observing that a(n) = 1 or a(n) = 2?

Examples

			a(1) = prime(1)! mod prime(1!) = 2 mod 2 = 0.
a(2) = prime(2)! mod prime(2!) = 6 mod 3 = 0.
a(3) = prime(3)! mod prime(3!) = 120 mod 13 = 3.
		

Crossrefs

Cf. A000040, A039716, A062439, A261997.

Programs

Magma

[Factorial(NthPrime(n)) mod NthPrime(Factorial(n)): n in [1..11]]; // Vincenzo Librandi, Sep 23 2015

Mathematica

Table[Mod[Prime[n]!, Prime[n!]], {n, 15}] (* Michael De Vlieger, Sep 21 2015 *)

PARI

a(n) = prime(n)! % prime(n!);
vector(11, n, a(n))

Formula

a(n) = A039716(n) mod A062439(n).

Extensions

a(11)-a(15) from Michael De Vlieger, Sep 21 2015