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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

Table of n, a(n) for n=1..7.

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.)