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A139074 a(n) = smallest prime p such that p!/n + 1 is prime, or 0 if no such prime exists. 36
2, 2, 3, 5, 7, 3, 11, 7, 26737, 5, 13, 5 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

For the corresponding primes p see A139075.

a(9)>5000, a(13)>5000, a(22)>5000, a(23) = 1579. - Andrew V. Sutherland (drew(AT)math.mit.edu), Apr 21 2008, Apr 22 2008

a(10)=5, a(11)=13, a(12)=5

a(14)= 17, a(15)=7, a(16)=13, a(17)=43, a(18)=7, a(19)=31, a(20)=5, a(21)=7

a(24)=7, a(25)=47, a(26)=17, a(27)=17, a(28)=7, a(29)=241, a(30)=5,

a(31)=61, a(32)=11, a(33)=17, a(34)=17, a(35)=29, a(36)=11, a(37)=61,

a(38)=103, a(39)=89, a(40)=7, a(41)=131, a(42)=11, a(43)=71, a(44)=13,

a(45)=7, a(46)=43, a(47)=73, a(48)=67, a(49)=347, a(50)=31, a(51)=19,

a(52)=17, a(53)=347, a(54)=11, a(55)=13, a(56)=13, a(57)=31, a(58)=73,

a(59)=641, a(60)=5

a(23) = 1579. - Andrew V. Sutherland (drew(AT)math.mit.edu), Apr 11 2008.

Smallest daughter factorial prime p of order n, i.e. smallest prime of the form (p!+n)/n where p is prime.

For smallest mother factorial prime p of order n see A139075

For smallest father factorial prime p of order n see A139207

For smallest son factorial prime p of order n see A139206

Summary added by Robert Price, Nov 25 2010:

a(1:20)=2,2,3,5,7,3,11,7,26737,5,13,5,>60000,17,7,13,43,7,31,5

a(21:40)=7,>60000,1579,7,47,17,17,7,241,5,61,11,17,17,29,11,61,103,89,7

a(41:60)=131,11,71,13,7,43,73,67,347,31,19,17,347,11,13,13,31,73,641,5

a(61:80)=89,31,13,13,17,11,71,19,131,7,151,7,>10000,641,73,43,17,331,113,11

a(81:100)=13,67,>10000,7,1999,89,31,11,>10000,19,19,31,607,71,61,11,761,23,>10000

,83

EXAMPLE

a(1) = 2 because 2 is the first prime and 2!/1 + 1 = 3 is prime

a(2) = 2 because 2 is the first prime and 2!/2 + 1 = 2 is prime

a(3) = 3 because 3!/3 + 1 = 3 is prime

MATHEMATICA

a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! + n)/n], k++ ]; AppendTo[a, Prime[k]], {n, 1, 8}]; a

CROSSREFS

Cf. A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139061, A139062, A139063, A139064, A139065, A139066, A020458, A139068, A137390, A139070, A139071, A139072, A139073, A139074, A139074, A139075, A136019, A136020, A136026, A136027.

Sequence in context: A032157 A153926 A035425 * A179418 A035428 A177851

Adjacent sequences:  A139071 A139072 A139073 * A139075 A139076 A139077

KEYWORD

more,nonn

AUTHOR

Artur Jasinski (grafix(AT)csl.pl), Apr 08 2008, Apr 21 2008

EXTENSIONS

a(9)-a(12) by Robert Price (pamandbobprice(AT)yahoo.com), Dec 19 2010

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Last modified February 15 04:23 EST 2012. Contains 205694 sequences.