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A078778
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Numbers n such that n!+1 is a semiprime.
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9
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4, 5, 6, 7, 8, 10, 13, 14, 19, 20, 24, 25, 26, 28, 34, 38, 48, 54, 55, 59, 71, 75, 92, 109, 114, 115
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OFFSET
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1,1
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COMMENTS
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Note that the two prime factors of 38!+1 = 523022617466601111760007224100074291200000001 = 14029308060317546154181 * 37280713718589679646221 both have 23 decimal digits. Are there any other terms in this sequence other than 4,5,7 and 38 with this property?
Other terms in this sequence: 392, 551, 601, 770, 772, 878, 1033, 1320, 1831, 2620, 2808, 3752, 4233, 4616, 4984, 7260. - Chai Wah Wu, Feb 28 2020
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LINKS
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EXAMPLE
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4 is in the sequence because 4!+1=25=5*5 is semiprime. But 9 is not in the sequence because 9!+1=19*71*269 is not semiprime. - Sean A. Irvine, Nov 15 2009
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MATHEMATICA
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Select[Range[100], Plus@@Last/@FactorInteger[#! + 1]==2 &] (* Vincenzo Librandi, May 26 2015 *)
Select[Range[100], PrimeOmega[#!+1]==2&] (* Harvey P. Dale, Mar 19 2017 *)
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PROG
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(PARI) { fp(a, b)=local(c, d, r); for(n=a, b, r=n!+1; c=vecmin(factor(r)[, 1]~); d=vecmax(factor(r)[, 1]~); if(bigomega(r)==2 && isprime(c) && isprime(d), print1(n" "); )) } fp(1, 100)
(Magma) IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [1..60] | IsSemiprime(Factorial(n)+1)]; // Vincenzo Librandi, May 26 2015
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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