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 A085700 Numbers n such that (2n)!-(2n-2)!+(2n-4)!-...+(-1)^n 0! is prime. 0
 2, 4, 26, 112, 365, 449, 453 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS EXAMPLE 4 is in the sequence because 8!-6!+4!-2!+1 =39623 is prime. MATHEMATICA Do[If[PrimeQ[Sum[(-1)^(n-k)(2k)!, {k, 0, n}]], Print[n], {n, 1000}] CROSSREFS Cf. A001272, A002981, A002982. Sequence in context: A259374 A155120 A144691 * A087404 A009237 A019019 Adjacent sequences:  A085697 A085698 A085699 * A085701 A085702 A085703 KEYWORD more,nonn AUTHOR Farideh Firoozbakht, Jul 18 2003 STATUS approved

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Last modified April 20 15:17 EDT 2021. Contains 343135 sequences. (Running on oeis4.)