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

1,1

Comments

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

References

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

Links

Table of n, a(n) for n=1..20.

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

Formula

When A014288(n-1) is prime.

Mathematica

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

Crossrefs

Cf. A014288, Left factorials: A003422.

See A124375 for another version.

Sequence in context: A112594 A188003 A120519 * A274231 A173999 A127427

Adjacent sequences: A100611 A100612 A100613 * A100615 A100616 A100617

Keyword

nonn,more

Author

R. K. Guy, Dec 02 2004

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

Status

approved