A242565 Numbers k such that (k!+1)/(k+1) is prime.

4, 6, 10, 28, 772, 1320, 2620

Offset

1,1

Comments

Subsequence of A006093.

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

a(8) > 4725.

If it exists, a(8) > 6778. - J.W.L. (Jan) Eerland, Aug 15 2022

Links

Table of n, a(n) for n=1..7.

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

Cf. A006093.

Sequence in context: A252656 A322961 A291542 * A032392 A253048 A271956

Adjacent sequences: A242562 A242563 A242564 * A242566 A242567 A242568

Keyword

nonn,more,hard

Author

Derek Orr, May 17 2014

Status

approved