A242915 Numbers n such that (n!-k!)/(n-k) is prime for some k.

2, 4, 5, 125

Offset

1,1

Comments

a(5) > 1000.

The n-values not listed have been checked for k <= 5000.

The number k that corresponds to {2, 4, 5, 125} is {4, 2, 125, 5} respectively.

Let S = (k!-n!)/(k-n). If n is in the sequence and k is the least number that makes S prime (using n), then n` = k is also in the sequence and k` = n is the least number that makes S prime (using n`).

Links

Table of n, a(n) for n=1..4.

Example

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

Prog

(PARI) a(n)=for(k=1, 5000, if(k!=n, s=(n!-k!)/(n-k); if(floor(s)==s&&ispseudoprime(s), return(k))))
n=1; while(n<1000, if(a(n), print1(n, ", ")); n+=1)

Crossrefs

Sequence in context: A065574 A247963 A105288 * A066684 A328784 A128124

Adjacent sequences: A242912 A242913 A242914 * A242916 A242917 A242918

Keyword

nonn,hard,more

Author

Derek Orr, May 26 2014

Status

approved