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Search: id:A078781
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| A078781 |
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Numbers n such that n!-1 is a semiprime. |
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+0
3
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| 5, 8, 10, 13, 16, 20, 23, 24, 26, 27, 34, 36, 40, 47, 50, 59, 68, 79, 85, 93, 137, 143
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The next candidate for a continuation is 151!-1, which is composite with 265 decimal digits and unknown factorization. Further known terms are: 157, 229, 381, 390, 392, 400, 814, 929, Factorization unknown for: 151, 154, 196, 232, 271, 307, 322, 332, 333, 334, 350, 352, 386, 389, 443, 449,...
Note that the two prime factors of 24!-1 = 620448401733239439359999 = 625793187653 * 991459181683 both have 12 decimal digits.
There is another term with prime factors with equal number of decimal digits: 34!-1=10398560889846739639*28391697867333973241 (20 digits each)
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LINKS
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Paul Leyland, Tables of factors of N!+1 and N!-1.
Andrew Walker, Factors of n!-1 for n>=400.
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PROGRAM
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(PARI) { fm(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(2, 100)
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CROSSREFS
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Cf. A001358, A080802.
Sequence in context: A084146 A087280 A022413 this_sequence A022160 A022158 A032717
Adjacent sequences: A078778 A078779 A078780 this_sequence A078782 A078783 A078784
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KEYWORD
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more,nonn,hard
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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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More terms from Hugo Pfoertner (hugo(AT)pfoertner.org), Apr 05 2003
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