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

%I A091415 #19 Mar 03 2017 12:23:26
%S A091415 2,3,4,8,13,32,41,45,59,97,107,364,421,444,1164,1663,3202,4335,4841,
%T A091415 13528,22159,38095,50327,72853
%N A091415 Numbers n such that n!*2^n - 1 is prime.
%H A091415 Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes.</a>
%H A091415 Ken Davis, <a href="http://mfprimes.free-dc.org/mfdata/f02m.html">Results for n!2-1.</a>
%F A091415 a(n) = A007749(n+1)/2. - _Alexander Adamchuk_, Sep 23 2006
%e A091415 a(1)=2 because 2!*2^2 - 1 = 7 is prime
%e A091415 a(2)=3 because 3!*2^3 - 1 = 47 is prime
%t A091415 For[n=1, n<1000,n++, If[PrimeQ[2^n*n!-1], Print[n]]] (Steinerberger)
%o A091415 (PARI) f(n)=n!*2^n -1; for (i=1,363,if(isprime(f(i)),print(i)))
%Y A091415 A093173 gives the corresponding primes.
%Y A091415 Cf. A007749, A117141, A092075.
%K A091415 hard,more,nonn
%O A091415 1,1
%A A091415 Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 02 2004
%E A091415 a(12)-a(14) from _Stefan Steinerberger_, Feb 05 2006
%E A091415 a(15) from Mohammed Bouayoun (Mohammed.Bouayoun(AT)yahoo.fr), Apr 13 2006
%E A091415 More terms from _Alexander Adamchuk_, Sep 23 2006
%E A091415 Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
%E A091415 Terms a(22)..a(24) (using A007749) from _Joerg Arndt_, Apr 22 2016