A082672 - OEIS

%I #27 Sep 08 2022 08:45:10

%S 2,4,5,7,8,13,16,30,43,49,91,119,213,1380,1637,2258,4647,9701,12258

%N Numbers n such that (n! + 2)/2 is a prime.

%t Select[Range[10^2], PrimeQ[(#!+2)/2] &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008 *)

%o (PARI) \\ x such that (x!+2)/2 is prime

%o xfactpk(n,k=2) = { for(x=2,n, y = (x!+k)/k; if(isprime(y),print1(x, ", ")) ) }

%o (Magma) [ n: n in [1..300] | IsPrime((Factorial(n)+2) div 2) ];

%Y Cf. A089130.

%Y Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, May 18 2003

%E More terms from _Don Reble_, Dec 08 2003

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008