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A100614 Numbers n such that (!n)/2 is prime, where !n = Sum_{k=0..n-1} k!. 2


%S 3,4,5,8,9,10,11,30,76,163,271,273,354,721,1796,3733,4769,9316,12221,

%T 41532

%N Numbers n such that (!n)/2 is prime, where !n = Sum_{k=0..n-1} k!.

%C No other terms below 50000. - _Serge Batalov_, Jul 23 2017

%D R. K. Guy, Unsolved Problems In Number Theory, B44.

%H Yves Gallot, <a href="http://perso.wanadoo.fr/yves.gallot/papers/lfact.html">Is the number of primes (of half the left handed factorials) finite?</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LeftFactorial.html">Left Factorial</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>

%F When A014288(n-1) is prime.

%t s = 1; Do[s = s + n!; If[ PrimeQ[s/2], Print[n + 1]], {n, 10^3}] (* _Robert G. Wilson v_, Dec 02 2004 *)

%Y Cf. A014288, Left factorials: A003422.

%Y See A124375 for another version.

%K nonn,more

%O 1,1

%A _R. K. Guy_, Dec 02 2004

%E a(14) from _Robert G. Wilson v_, Dec 02 2004

%E a(15)=1796 from _Ray Chandler_, Dec 02 2004

%E a(17) from _T. D. Noe_, Dec 04 2004

%E Corrected by adding a(16)=3733 from _Eric W. Weisstein_, Oct 29 2005

%E a(18)=9316 from _Eric W. Weisstein_, Dec 27 2005

%E a(19)=12221 from _Eric W. Weisstein_, Oct 19 2006

%E a(20)=41532 from _Serge Batalov_, Jul 22 2017

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)