

A242565


Numbers k such that (k!+1)/(k+1) is prime.


1




OFFSET

1,1


COMMENTS

It is unknown whether this sequence is infinite. If S = (n!+k)/(n+k), when k > 1, there are finitely many nvalues that make S an integer. When k = 1, there are infinitely many nvalues that make S an integer (A006093).
a(8) > 4725.


LINKS



EXAMPLE

(4!+1)/(4+1) = 5 is prime. Thus, 4 is a member of this sequence.


MATHEMATICA

ParallelTable[If[PrimeQ[(Factorial[n]+1)/(n+1)], n, Nothing], {n, 1, 5*10^3}]//.{}>Nothing (* J.W.L. (Jan) Eerland, Aug 15 2022 *)


PROG

(PARI) for(n=1, 5000, s=((prime(n)1)!+1)/(prime(n)); if(ispseudoprime(s), print1(prime(n)1)))


CROSSREFS



KEYWORD

nonn,more,hard


AUTHOR



STATUS

approved



