A151900 -id:A151900 - cp's OEIS frontend

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

Artur Jasinski, Apr 11 2008, Apr 24 2008

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

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

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

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

Edited by M. F. Hasler, Nov 03 2013

A151901 Singular indices in A139074.

Original entry on oeis.org

9, 13, 22, 23, 72, 73, 74, 82, 83, 84, 85, 88

Offset: 1

Artur Jasinski, Apr 12 2008

nonn

Definition: Singular indices in A139074 are numbers n such that it doesn't exist a prime p such that (n+p!)/n is prime or if this prime does exist then it is very big.

Cf. A139074, A139206, A151900.

cp's OEIS Frontend

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

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