A073308 Numbers k such that k! + k + 1 is prime.

0, 1, 2, 4, 6, 10, 52, 6822, 30838

Offset: 1

Author

Rick L. Shepherd, Jul 24 2002

Keywords

• nonn
• more

Comments

Clearly, for k>2, k != 2 (mod 3).

Often m! + 2, m! + 3, ..., m! + m is cited as a constructed sequence of m-1 consecutive composite numbers.

Except for 0, k+1 is prime. - Robert Israel, Jan 13 2015

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 52, p. 20, Ellipses, Paris 2008.

Crossrefs

Cf. A073309 (corresponding primes), A002981 (n!+1 is prime), A073443 (n!-n-1 is prime), A092791.

Programs

Mathematica

f[n_]:=n!+n+1; lst={};Do[p=f[n];If[PrimeQ[p],AppendTo[lst,n]],{n,0,2*5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 02 2009 *)

PARI

for(n=0,1960,if(isprime(n!+n+1),print1(n,",")))

Formula

a(n) = A092791(n) - 1. - Seiichi Manyama, Mar 19 2018

Extensions

a(8) from T. D. Noe, Jan 18 2008

a(9) from Seiichi Manyama (by using the data calculated by Giovanni Resta, May 04 2013), Mar 19 2018