

A242457


Least number k such that k!/n is prime, or 0 if no such number exists.


2



2, 3, 3, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

a(n) <= n + 2 for all n > 0.


LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000


EXAMPLE

a(3) = 3 because 3!/3 = 6/3 = 2, which is prime.
a(4) = 0 because there is no k such that k!/4 is a prime. For all k > 3, k! has 24 as a divisor, so therefore k!/4 has 6 as a divisor and is therefore certainly composite.


MAPLE

N:= 7: # to get all a(n) for n <= N!
A:= Array(1..N!):
for k from 1 to N do
for p in select(isprime, [$2..k]) do
if A[k!/p] = 0 then A[k!/p]:= k fi
od
od:
seq(A[n], n=1..N!); # Robert Israel, Aug 18 2014


PROG

(PARI)
a(n)=for(k=1, n+2, s=k!/n; if(floor(s)==s, if(ispseudoprime(s), return(k))))
n=1; while(n<100, print1(a(n), ", "); n++)


CROSSREFS

Cf. A242456.
Sequence in context: A075108 A265590 A260208 * A190146 A026932 A087401
Adjacent sequences: A242454 A242455 A242456 * A242458 A242459 A242460


KEYWORD

nonn


AUTHOR

Derek Orr, Aug 16 2014


STATUS

approved



