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A245757 Numbers n such that (k!+n)/k is never prime for any k. 2
5, 7, 11, 13, 14, 17, 19, 21, 23, 26, 29, 31, 34, 37, 39, 41, 43, 47, 48, 50, 53, 54, 55, 57, 59, 61, 62, 64, 67, 69, 71, 73, 75, 76, 77, 79, 83, 86, 89, 90, 93, 94, 97, 98, 99, 101, 103, 107, 109, 110, 111, 113, 118, 119, 122, 125, 127, 128, 129, 131, 134, 137, 139, 141, 142, 143, 146 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

k <= n for all n so k can only be a finite set of numbers.

Only k dividing n need be considered.

By Wilson's theorem, all primes > 3 are in the sequence. - Robert Israel, Jul 31 2014

LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 1..1000

EXAMPLE

(1!+5)/1 = 6 is not prime.

(2!+5)/2 = 7/2 is not prime.

(3!+5)/3 = 11/3 is not prime.

(4!+5)/4 = 29/4 is not prime.

(5!+5)/5 = 25 is not prime.

For any k > 5, (k!+5)/k = (k-1)! + 5/k will always be a fraction and thus, never prime. So 5 is a member of this sequence.

MAPLE

filter:= proc(n) local k;

  for k in numtheory:-divisors(n) do

     if isprime((k!+n)/k) then return false fi

  od:

  true

end proc:

select(filter, [$1..1000]); # Robert Israel, Jul 31 2014

PROG

(PARI)

a(n)=for(k=1, n, s=(k!+n)/k; if(floor(s)==s, if(ispseudoprime(s), return(k))))

n=1; while(n<200, if(!a(n), print1(n, ", ")); n++)

CROSSREFS

Cf. A245756.

Sequence in context: A098761 A113837 A255363 * A240912 A263080 A280199

Adjacent sequences:  A245754 A245755 A245756 * A245758 A245759 A245760

KEYWORD

nonn

AUTHOR

Derek Orr, Jul 31 2014

STATUS

approved

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Last modified May 29 10:41 EDT 2020. Contains 334699 sequences. (Running on oeis4.)