OFFSET
1,1
COMMENTS
Sum_{i=0..k} i! = k! + !k = A003422(k+1), where !k is left factorial !k = Sum_{i=0..k-1} i! = A003422(k). Left factorials are even for k > 1. Corresponding primes of the form (k! + !k)/2 = (a(n)! + !a(n))/2 are listed in A124374(n) = {2, 5, 17, 2957, 23117, 204557, 2018957, 4578979328975537786697650470157, ...}.
LINKS
Hisanori Mishima, Factorizations of many number sequences.
Eric Weisstein's World of Mathematics, Left Factorial.
MATHEMATICA
f=0; Do[f=f+n!; If[PrimeQ[f/2], Print[{n, f/2}]], {n, 0, 353}]
Flatten[Position[Accumulate[(Range[0, 12220]!)]/2, _?PrimeQ]]-1 (* Harvey P. Dale, Jul 02 2019 *)
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Alexander Adamchuk, Oct 28 2006
EXTENSIONS
More terms from Ryan Propper, Feb 07 2008
a(20) from Jinyuan Wang, Mar 20 2021
STATUS
approved