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A085700
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Numbers n such that (2n)!-(2n-2)!+(2n-4)!-...+(-1)^n 0! is prime.
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0
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OFFSET
| 1,1
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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.
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EXAMPLE
| 4 is in the sequence because 8!-6!+4!-2!+1 =39623 is prime.
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MATHEMATICA
| Do[If[PrimeQ[Sum[(-1)^(n-k)(2k)!, {k, 0, n}]], Print[n], {n, 1000}]
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CROSSREFS
| Cf. A001272, A002981, A002982.
Sequence in context: A028386 A155120 A144691 * A087404 A009237 A019019
Adjacent sequences: A085697 A085698 A085699 * A085701 A085702 A085703
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KEYWORD
| more,nonn
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AUTHOR
| Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Jul 18 2003
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