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

1,1

Links

Table of n, a(n) for n=1..24.

Ken Davis, Status of Search for Multifactorial Primes.

Ken Davis, Results for n!2-1.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

A093173 gives the corresponding primes.

Cf. A007749, A117141, A092075.

Sequence in context: A186272 A361722 A092075 * A166342 A361502 A091816

Adjacent sequences: A091412 A091413 A091414 * A091416 A091417 A091418

Keyword

hard,more,nonn

Author

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

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

Status

approved