A140294 Numbers n such that n!/n# + 1 is prime, where n# is the primorial function (A034386).

0, 1, 2, 3, 4, 5, 8, 14, 20, 26, 34, 56, 104, 153, 182, 194, 217, 230, 280, 281, 462, 463, 529, 1445, 2515, 3692, 6187, 6851, 13917, 17258, 48934

Offset

1,3

Comments

96835 is a term of the sequence, but its rank is not currently known. - Serge Batalov, Feb 06 2015

Links

Table of n, a(n) for n=1..31.

Chris Caldwell, Compositorial

Example

8!/8# + 1 = 40320/210 + 1 = 193, a prime.

Maple

A140294 := proc(n) local L, p, s, i; L := 1;
for p in select(isprime, [$2..iquo(n, 2)]) do
    s := add(i, i=convert(n, base, p)); L := L*p^((n-s)/(p-1)-1) od;
`if`(isprime(L+1), n, NULL) end:
seq(A140294(i), i=0..104); # Peter Luschny, Mar 27 2013

Mathematica

Primorial[p_] := Times @@ Prime[Range[PrimePi[p]]]; Select[Range[0, 194], PrimeQ[#!/Primorial[#] + 1] &] (* T. D. Noe, Mar 27 2013 *)

Prog

(PARI) is(n)=ispseudoprime(n!/prod(i=1, primepi(n), prime(i))+1) \\ Charles R Greathouse IV, Mar 27 2013
(PFGW) ABC2 $a!/$a#+1
a: from 1 to 3000

Crossrefs

Cf. A034386, A140293, A140315, A049420, A049421.

Sequence in context: A333785 A162900 A015925 * A108014 A075721 A112479

Adjacent sequences: A140291 A140292 A140293 * A140295 A140296 A140297

Keyword

nonn

Author

Cino Hilliard, May 25 2008

Extensions

a(17)-a(25) from Charles R Greathouse IV, Mar 27 2013

a(26)-a(27) from Giovanni Resta, Mar 28 2013

a(28) from Charles R Greathouse IV, Mar 28 2013

a(29) from Giovanni Resta, Apr 02 2013

a(30) from Roger Karpin, Nov 29 2014

a(31) from Roger Karpin, Jun 08 2015

Status

approved