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A242915 Numbers n such that (n!-k!)/(n-k) is prime for some k. 0
2, 4, 5, 125 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(5) > 1000.
The n-values not listed have been checked for k <= 5000.
The number k that corresponds to {2, 4, 5, 125} is {4, 2, 125, 5} respectively.
Let S = (k!-n!)/(k-n). If n is in the sequence and k is the least number that makes S prime (using n), then n` = k is also in the sequence and k` = n is the least number that makes S prime (using n`).
LINKS
EXAMPLE
(4!-k!)/(4-k) is prime for some k (namely, k = 2). Thus 4 is a member of this sequence.
PROG
(PARI) a(n)=for(k=1, 5000, if(k!=n, s=(n!-k!)/(n-k); if(floor(s)==s&&ispseudoprime(s), return(k))))
n=1; while(n<1000, if(a(n), print1(n, ", ")); n+=1)
CROSSREFS
Sequence in context: A065574 A247963 A105288 * A066684 A328784 A128124
KEYWORD
nonn,hard,more
AUTHOR
Derek Orr, May 26 2014
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)