A139206 Smallest son factorial prime p of order n: smallest p such that p!/n-1 is prime.

3, 3, 29, 5, 5, 5, 7, 11, 17, 5, 19, 7, 13, 7, 5, 37, 139, 19

Offset: 1

Author

Artur Jasinski, Apr 11 2008, Apr 24 2008

Keywords

• hard
• more
• nonn

Comments

For smallest daughter factorial prime p of order n (smallest p such that (p!+n)/n = p!/n + 1 is prime), see A139074.

a(19) is currently unknown, a(20)=5, a(21)=7, a(22)=19.

a(19)>10000, a(23)=71, a(24)=3361. [From Andrew V. Sutherland, Apr 23 2008]

a(25)=17, a(26)=223, a(27)=157, a(28)=7, a(29)=41, a(30)=5, a(31)=31, a(32)=71, a(33)=13, a(34)=37, a(35)=19, a(36)=7, a(37)=47, a(38)=53, a(39)=13, a(40)=5, a(41)=127, a(42)=13, a(43)=67, a(44)=11, a(45)=17, a(46)=43, a(47)=71, a(48)=11, a(49)=19, a(50)=29, a(51)=17, a(52)=17, a(53)>10000.

a(19)>25000, a(53)>25000. [From Sean A. Irvine, Nov 14 2010]

a(54)=11, a(55)=23, a(56)=7, a(57)=433.

a(58)=283, a(59)>1500, a(60..66)=(7,139,239,7,11,13,13), a(67), a(68) > 1300, a(69..72)=(29,7,83,13), a(73)>1000. [From M. F. Hasler, Nov 03 2013]

Sequence A151900 (tentatively?) lists "singular indices", i.e., those for which a(n) is difficult to find. - M. F. Hasler, Nov 03 2013

Crossrefs

Cf. A139074, A139189-A139198, A136019, A136020, A136026, A136027.

Programs

Mathematica

a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! - n)/n], k++ ]; Print[a]; AppendTo[a, Prime[k]], {n, 1, 100}]; a (*Artur Jasinski*)

PARI

a(n)=forprime(p=1,,p!%n==0 && ispseudoprime(p!/n-1) && return(p)) \\ - M. F. Hasler, Nov 03 2013

Extensions

Edited by M. F. Hasler, Nov 03 2013