A242457 Least number k such that k!/n is prime, or 0 if no such number exists.

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

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: A364139 A265590 A260208 * A340261 A190146 A026932

Adjacent sequences: A242454 A242455 A242456 * A242458 A242459 A242460

Keyword

nonn

Author

Derek Orr, Aug 16 2014

Status

approved