

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 = (k1)! + 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



