A100614 Numbers n such that (!n)/2 is prime, where !n = Sum_{k=0..n-1} k!.

3, 4, 5, 8, 9, 10, 11, 30, 76, 163, 271, 273, 354, 721, 1796, 3733, 4769, 9316, 12221, 41532

Offset: 1

Author

R. K. Guy, Dec 02 2004

Keywords

• nonn
• more

Comments

No other terms below 50000. - Serge Batalov, Jul 23 2017

References

• R. K. Guy, Unsolved Problems In Number Theory, B44.

Links

• Yves Gallot, Is the number of primes (of half the left handed factorials) finite?.
• Eric Weisstein's World of Mathematics, Left Factorial
• Eric Weisstein's World of Mathematics, Integer Sequence Primes

Crossrefs

Cf. A014288, Left factorials: A003422.

See A124375 for another version.

Programs

Mathematica

s = 1; Do[s = s + n!; If[ PrimeQ[s/2], Print[n + 1]], {n, 10^3}] (* Robert G. Wilson v, Dec 02 2004 *)

Formula

When A014288(n-1) is prime.

Extensions

a(14) from Robert G. Wilson v, Dec 02 2004

a(15)=1796 from Ray Chandler, Dec 02 2004

a(17) from T. D. Noe, Dec 04 2004

Corrected by adding a(16)=3733 from Eric W. Weisstein, Oct 29 2005

a(18)=9316 from Eric W. Weisstein, Dec 27 2005

a(19)=12221 from Eric W. Weisstein, Oct 19 2006

a(20)=41532 from Serge Batalov, Jul 22 2017