A093173 Primes of the form (2^n * n!) - 1.

7, 47, 383, 10321919, 51011754393599, 1130138339199322632554990773529330319359999999, 73562883979319395645666688474019139929848516028923903999999999, 4208832729023498248022825567687608993477547383960134557368319999999999

Offset: 1

Author

Enoch Haga, Mar 27 2004

Keywords

• nonn

Comments

Primes resulting from serial multiplication of even numbers, minus 1.

For primes of the form 2^n*n! + 1, trivially a(1)=3, a(2) = 2^259*259! + 1 (593 digits). - Ray Chandler, Mar 27 2004

Examples

			a(1) multiplies the first 2 terms, 2*4-1. a(3) multiplies first 4 terms, a(4) multiplies first 8 terms, a(5) multiplies first 13 terms in 12 multiplications.
a(2)=47, formed by 2*4*6 - 1 = 47.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..12

Crossrefs

Cf. A093154, A093155.

Cf. A117141 (primes of the form n!! - 1).

Programs

Mathematica

lst={};Do[If[PrimeQ[p=(2^n*n!)-1],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)

PARI

v=[];for(n=1,404,if(ispseudoprime(t=n!<Charles R Greathouse IV, Feb 14 2011

Formula

Starting with 2, multiply even numbers until the product, minus 1, equals a prime.

a(n) = A117141(n+1). - Alexander Adamchuk, Apr 18 2007

Extensions

More terms from Ray Chandler, Mar 27 2004

a(8) from Robert Price, Mar 13 2015