The On-Line Encyclopedia of Integer Sequences (OEIS)

A139056 revision #41

A139056

Numbers k for which (k!-3)/3 is prime.

4, 6, 12, 16, 29, 34, 43, 111, 137, 181, 528, 2685, 39477, 43697

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OFFSET

1,1

COMMENTS

Corresponding primes (k!-3)/3 are in A139057.

a(13) > 10000. The PFGW program has been used to certify all the terms up to a(12), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Mar 28 2014

98166 is a member of the sequence but its index is not yet determined. The interval where sieving and tests were not run is 60000..90000. - Serge Batalov, Feb 24 2015

LINKS

Table of n, a(n) for n=1..14.

C. Caldwell. The Prime database entry for the prime generated by a(i)=98166.

MATHEMATICA

a = {}; Do[If[PrimeQ[(-3 + n!)/3], AppendTo[a, n]], {n, 1, 1000}]; a

PROG

(PARI) for(n=1, 1000, if(floor(n!/3-1)==n!/3-1, if(ispseudoprime(n!/3-1), print(n)))) \\ Derek Orr, Mar 28 2014

CROSSREFS

Cf. A007749, A117141.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205.

Cf. n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071.

Cf. m*n!-1 is a prime: A076133, A076134, A099350, A099351, A180627-A180631.