A239942 a(n) = prime(n)! - prime(n - 1)!.

4, 114, 4920, 39911760, 6187104000, 355681201075200, 121289412980736000, 25851895093784567808000, 8841761967887685215658639360000, 8213996892184183115771019264000000, 13763753083003506392138056763855339520000000

Offset: 2

Author

Norman Koch, Mar 29 2014

Keywords

• nonn

Examples

			a(3) = Prime(3)! - Prime(2)! = 5! - 3! = 120 - 6 = 114.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..87

Crossrefs

Cf. A000040, A039716.

Programs

Maple

A239942:=n->ithprime(n)!-ithprime(n-1)!: seq(A239942(n), n=2..15); # Wesley Ivan Hurt, Aug 03 2014

Mathematica

a239942[n_Integer] := Prime[n]! - Prime[n - 1]!; Table[a239942[n], {n, 2, 87}] (* Michael De Vlieger, Aug 03 2014 *)

PARI

a(n)=prime(n)! - prime(n-1)!;
vector(22,n,a(n+1)) \\ Joerg Arndt, Mar 31 2014

Perl

#!/usr/bin/perl
use strict;
use warnings;
use feature 'say';
use Math::Prime::XS qw(is_prime);
use Memoize;
use Math::BigInt;
memoize('factorial');
use Data::Dumper;
my @primes = ();
for (2 .. 200) {
        if(is_prime($_)) {
                push @primes, $_;
        }
}
for (1 .. $#primes) {
        say factorial($primes[$]) - factorial($primes[$ - 1]);
}
sub factorial {
        my $x = Math::BigInt->new(shift);
        return $x if $x == 1;
        return factorial($x - 1) * $x;
}

Python

from gmpy2 import mpz,fac
from sympy import prime
def A239942(n):
    return fac(mpz(prime(n))) - fac(mpz(prime(n-1))) # Chai Wah Wu, Aug 06 2014

Formula

a(n) = A039716(n) - A039716(n-1).