A073308 - OEIS

%I #38 Mar 22 2018 10:22:44

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

%N Numbers k such that k! + k + 1 is prime.

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

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

%C Except for 0, k+1 is prime. - _Robert Israel_, Jan 13 2015

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

%F a(n) = A092791(n) - 1. -  _Seiichi Manyama_, Mar 19 2018

%t 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 *)

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

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

%K nonn,more

%O 1,3

%A _Rick L. Shepherd_, Jul 24 2002

%E a(8) from _T. D. Noe_, Jan 18 2008

%E a(9) from _Seiichi Manyama_ (by using the data calculated by _Giovanni Resta_, May 04 2013), Mar 19 2018