%I A001272
%S A001272 3,4,5,6,7,8,10,15,19,41,59,61,105,160,661,2653,3069,3943,4053,4998,
%T A001272 8275,9158,11164
%N A001272 Numbers n such that n!-(n-1)!+(n-2)!-(n-3)!+...+-1! is prime.
%C A001272 At present the terms >= 2653 are only probable primes.
%C A001272 Zivkovic shows that all terms must be less than p=3612703, which divides 
               a(n) for n>=p. - T. D. Noe (noe(AT)sspectra.com), Jan 25 2008
%D A001272 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 160, p. 52, Ellipses, 
               Paris 2008.
%D A001272 Martin Gardner, Strong Laws of Small Primes, in The Last Recreations, 
               p. 198 (1997).
%D A001272 R. K. Guy, Unsolved Problems in Number Theory, B43.
%D A001272 M. Zivkovi\'c, The number of primes $ Sum\sp n\sb {i=1}(-1)\sp {n-i}i!$ 
               is finite. Math. Comp. 68 (1999), no. 225, 403-409.
%H A001272 R. Ondrejka, <a href="http://www.utm.edu/research/primes/lists/top_ten/
               ">The Top Ten: a Catalogue of Primal Configurations</a>
%H A001272 Titanix, <a href="http://www.znz.freesurf.fr/files/titanix.zip">Primality 
               proof for n=661</a>
%H A001272 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FactorialSums.html">Factorial Sums</a>
%H A001272 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H A001272 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%H A001272 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AlternatingFactorial.html">Alternating Factorial</a>
%p A001272 with(numtheory); f := proc(n) local i; add((-1)^(n-i)*i!,i=1..n); end; 
               isprime(f(15));
%Y A001272 Cf. A005165, A002981, A002982.
%Y A001272 Cf. A100289.
%Y A001272 Sequence in context: A066378 A125684 A089358 this_sequence A047563 A120561 
               A051016
%Y A001272 Adjacent sequences: A001269 A001270 A001271 this_sequence A001273 A001274 
               A001275
%K A001272 nonn,hard,nice,fini
%O A001272 1,1
%A A001272 N. J. A. Sloane (njas(AT)research.att.com).
%E A001272 661 found independently by Eric Weisstein (eric(AT)weisstein.com) and 
               Rachel Lewis (racheljlewis(AT)hotmail.com); 2653 and 3069 found independently 
               by Chris Nash (nashc(AT)lexmark.com) and Rachel Lewis (racheljlewis(AT)hotmail.com).
%E A001272 3943, 4053, 4998 found by Paul Jobling (paul.jobling(AT)whitecross.com).
%E A001272 8275, 9158 found by team of Rachel Lewis, Paul Jobling and Chris Nash.
%E A001272 661!-660!+659!-... was shown to be prime by team of Giovanni La Barbera 
               and others using the Certifix program developed by Marcel Martin, 
               Jul 15 2000 (see link) - Paul Jobling (Paul.Jobling(AT)WhiteCross.com) 
               and Giovanni La Barbera, Aug 02 2000
%E A001272 a(23)=11164 found by Paul Jobling on Nov 25 2004.
%E A001272 Edited by T. D. Noe (noe(AT)sspectra.com), Oct 30 2008