A139199 Numbers k such that (k!-4)/4 is prime.

4, 5, 6, 7, 8, 10, 15, 18, 23, 157, 165, 183, 184, 362, 611, 908, 2940, 6875, 9446, 16041

Offset: 1

Author

Artur Jasinski, Apr 11 2008

Keywords

• hard
• more
• nonn

Comments

Numbers k such that (k!-m)/m is prime:

for m=1 see A002982

for m=2 prime or pseudoprime see A082671

for m=3 see A139056

for m=4 see A139199

for m=5 see A139200

for m=6 see A139201

for m=7 see A139202

for m=8 see A139203

for m=9 see A139204

for m=10 see A139205

a(17) > 2000 - Ray G. Opao, Sep 30 2008

a(21) > 25000 - Robert Price, Sep 25 2016

Crossrefs

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

Programs

Mathematica

a = {}; Do[If[PrimeQ[(n! - 4)/4], Print[a]; AppendTo[a, n]], {n, 1, 184}]; a (*Artur Jasinski*)

PARI

is(n)=n>3 && isprime(n!/4-1) \\ Charles R Greathouse IV, Apr 29 2015

Extensions

a(15)-a(16) from Ray G. Opao, Sep 30 2008

a(17) from Serge Batalov, Feb 18 2015

a(18)-a(20) from Robert Price, Sep 25 2016