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

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

Offset

2,1

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A039716.

Sequence in context: A194495 A260575 A275747 * A261457 A080482 A340277

Adjacent sequences: A239939 A239940 A239941 * A239943 A239944 A239945

Keyword

nonn

Author

Norman Koch, Mar 29 2014

Status

approved