%I A085700
%S A085700 2,4,26,112,365,449,453
%N A085700 Numbers n such that (2n)!-(2n-2)!+(2n-4)!-...+(-1)^n 0! is prime.
%C A085700 There is no further term up to 1000. Consider that 3 divides n!+(n-1)!+(n-2)!+...+1! 
               (n > 1), so this number is composite for n > 2. Also 5 divides n!-(n-1)!+...+(-1)^n*1! 
               for n > 2, so this number is composite for n > 3.
%e A085700 4 is in the sequence because 8!-6!+4!-2!+1 =39623 is prime.
%t A085700 Do[If[PrimeQ[Sum[(-1)^(n-k)(2k)!, {k, 0, n}]], Print[n], {n, 1000}]
%Y A085700 Cf. A001272, A002981, A002982.
%Y A085700 Sequence in context: A028386 A155120 A144691 this_sequence A087404 A009237 
               A019019
%Y A085700 Adjacent sequences: A085697 A085698 A085699 this_sequence A085701 A085702 
               A085703
%K A085700 more,nonn
%O A085700 1,1
%A A085700 Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Jul 18 2003