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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
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.
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
KEYWORD
more,nonn
AUTHOR
Farideh Firoozbakht, Jul 18 2003
STATUS
approved