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A239412
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Numbers n such that (n!-k)/(n-k) is prime for some k.
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0
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4, 6, 8, 16, 18, 92, 254, 258, 660, 1850, 2496, 2774, 2832, 7430, 28540, 32124
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OFFSET
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1,1
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COMMENTS
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a(14) > 3000.
There is only one value of k that can work, and it is n/2. Thus, all members of the sequence are even.
Even numbers n such that 2*(n-1)!-1 is prime.
(Odd members of A076133) + 1. - Robert Israel, Aug 11 2016
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LINKS
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Table of n, a(n) for n=1..16.
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EXAMPLE
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(4!-k)/(4-k) is prime for some k (namely, k = 2). Thus, 4 is a member of this sequence.
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MAPLE
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select(t -> isprime(2*(t-1)!-1), [seq(q, q=2..1000, 2)]); # Robert Israel, Aug 11 2016
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MATHEMATICA
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Select[Range[2, 10^3, 2], PrimeQ[2 (# - 1)! - 1] &] (* Michael De Vlieger, Aug 11 2016 *)
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PROG
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(PARI) a(n)=for(k=1, int(n/2), s=(n!-k)/(n-k); if(floor(s)==s, if(ispseudoprime(s), return(k))))
n=1; while(n<1000, if(a(n), print1(n, ", ")); n+=1)
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CROSSREFS
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Cf. A076133.
Sequence in context: A095299 A079250 A055397 * A295006 A269833 A049421
Adjacent sequences: A239409 A239410 A239411 * A239413 A239414 A239415
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KEYWORD
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nonn,hard,more
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AUTHOR
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Derek Orr, May 26 2014
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EXTENSIONS
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Edited and a(14)-a(16) added by Robert Israel, Aug 11 2016
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STATUS
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approved
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