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A239412 Numbers n such that (n!-k)/(n-k) is prime for some k. 0
4, 6, 8, 16, 18, 92, 254, 258, 660, 1850, 2496, 2774, 2832, 7430, 28540, 32124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

(4!-k)/(4-k) is prime for some k (namely, k = 2). Thus, 4 is a member of this sequence.

MAPLE

select(t -> isprime(2*(t-1)!-1), [seq(q, q=2..1000, 2)]); # Robert Israel, Aug 11 2016

MATHEMATICA

Select[Range[2, 10^3, 2], PrimeQ[2 (# - 1)! - 1] &] (* Michael De Vlieger, Aug 11 2016 *)

PROG

(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)

CROSSREFS

Cf. A076133.

Sequence in context: A095299 A079250 A055397 * A295006 A269833 A049421

Adjacent sequences:  A239409 A239410 A239411 * A239413 A239414 A239415

KEYWORD

nonn,hard,more

AUTHOR

Derek Orr, May 26 2014

EXTENSIONS

Edited and a(14)-a(16) added by Robert Israel, Aug 11 2016

STATUS

approved

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Last modified October 19 23:51 EDT 2021. Contains 348095 sequences. (Running on oeis4.)