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Smallest son factorial prime p of order n: smallest p such that p!/n-1 is prime.
5

%I #16 Nov 05 2013 06:28:21

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

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

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

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

%C a(19)>10000, a(23)=71, a(24)=3361. [From _Andrew V. Sutherland_, Apr 23 2008]

%C 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.

%C a(19)>25000, a(53)>25000. [From _Sean A. Irvine_, Nov 14 2010]

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

%C 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]

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

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

%o (PARI) a(n)=forprime(p=1,,p!%n==0 && ispseudoprime(p!/n-1) && return(p)) \\ - _M. F. Hasler_, Nov 03 2013

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

%K hard,more,nonn

%O 1,1

%A _Artur Jasinski_, Apr 11 2008, Apr 24 2008

%E Edited by _M. F. Hasler_, Nov 03 2013