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A050299
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Numbers n such that ((n-1)!+1)/n is prime.
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4
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OFFSET
| 1,2
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COMMENTS
| Except for the first term, all terms are primes because for n > 1, n divides (n-1)!+1 iff n is prime. There are no other terms up to 6550 and the corresponding next prime has more than 22150 digits.
No more terms below 30941.
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REFERENCES
| Javier Soria, posting to Number Theory List, Apr 08 2003
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LINKS
| Mike Oakes, posting to Number Theory List, Aug 20 2003
J. Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, in Proceedings of CANT 2011, arXiv:1110.3113
Javier Soria, posting to Number Theory List, Apr 08 2003
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FORMULA
| ((a(n)-1)!+1)/a(n) = A122696(n) = A007619(A000720(A050299(n))) for n > 1. [Jonathan Sondow, Aug 07 2011]
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EXAMPLE
| 7 is in the sequence because (6!+1)/7=103 is prime.
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MATHEMATICA
| v={1}; Do[If[PrimeQ[((Prime[n]-1)!+1)/Prime[n]], v=Append[v, Prime[n]]; Print[v]], {n, 845}]
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CROSSREFS
| Sequence in context: A031134 A144231 * A092029 A156559 A018426 A038976
Adjacent sequences: A050296 A050297 A050298 * A050300 A050301 A050302
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 09 2003
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EXTENSIONS
| 1321 and 2621 from Mike Oakes, Aug 20 2003
Additional comments from Farideh Firoozbakht (mymontain(AT)yahoo.com), Mar 19 2004
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