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Search: id:A078778
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| A078778 |
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Numbers n such that n!+1 is a semiprime. |
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+0
5
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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?
It is likely that 114 and 115 are the next terms. [Sean A. Irvine (sairvin(AT)xtra.co.nz), Nov 15 2009]
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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 (sairvin(AT)xtra.co.nz), Nov 15 2009]
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PROGRAM
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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)
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CROSSREFS
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Cf. A001358, A082952, A090159, A090160, A078781.
Adjacent sequences: A078775 A078776 A078777 this_sequence A078779 A078780 A078781
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KEYWORD
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more,nonn,new
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Jan 09 2003
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EXTENSIONS
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One more term (109) from Sean A. Irvine (sairvin(AT)xtra.co.nz), Nov 15 2009
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