A091415 Numbers n such that n!*2^n - 1 is prime.

2, 3, 4, 8, 13, 32, 41, 45, 59, 97, 107, 364, 421, 444, 1164, 1663, 3202, 4335, 4841, 13528, 22159, 38095, 50327, 72853

Offset: 1

Author

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 02 2004

Keywords

• hard
• more
• nonn

Examples

			a(1)=2 because 2!*2^2 - 1 = 7 is prime
a(2)=3 because 3!*2^3 - 1 = 47 is prime
		

Links

• Ken Davis, Status of Search for Multifactorial Primes.
• Ken Davis, Results for n!2-1.

Crossrefs

A093173 gives the corresponding primes.

Cf. A007749, A117141, A092075.

Programs

Mathematica

For[n=1, n<1000,n++, If[PrimeQ[2^n*n!-1], Print[n]]] (Steinerberger)

PARI

f(n)=n!*2^n -1; for (i=1,363,if(isprime(f(i)),print(i)))

Formula

a(n) = A007749(n+1)/2. - Alexander Adamchuk, Sep 23 2006

Extensions

a(12)-a(14) from Stefan Steinerberger, Feb 05 2006

a(15) from Mohammed Bouayoun (Mohammed.Bouayoun(AT)yahoo.fr), Apr 13 2006

More terms from Alexander Adamchuk, Sep 23 2006

Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

Terms a(22)..a(24) (using A007749) from Joerg Arndt, Apr 22 2016