A092789 a(n) = smallest prime of the form prime(n)+m! for some m >= 0.

3, 5, 7, 13, 13, 19, 19, 43, 29, 31, 37, 43, 43, 67, 53, 59, 61, 67, 73, 73, 79, 103, 89, 113, 103, 103, 109, 109, 229, 137, 151, 137, 139, 163, 151, 157, 163, 283, 173, 179, 181, 363061, 193, 199, 199, 223, 331, 229, 229, 349, 239, 241, 5281, 257, 263, 269, 271

Offset: 1

Author

Cino Hilliard, Apr 14 2004

Keywords

• nonn

Comments

n! + p is composite for n >= p since p divides n! for n >= p.

Is it known that such a prime always exists? If not the definition should say "or -1 if no such prime exists". - N. J. A. Sloane, Aug 11 2011

Crossrefs

Cf. A175193, A175194, A082470.

Programs

Magma

SmallestP:=function(p) for m in [0..p-1] do q:=p+Factorial(m); if IsPrime(q) then return q; end if; end for; return -1; end function; [ SmallestP(NthPrime(n)): n in [1..80] ]; // Klaus Brockhaus, Mar 02 2010

Maple

A092789 := proc(n) local q,m ; for m from 0 do q := ithprime(n)+m! ; if isprime(q) then return q; end if; end do ; end proc:
seq(A092789(n),n=1..80) ; # R. J. Mathar, Mar 02 2010

PARI

nfactpm3(n) = { forprime(p=1,n, c=0; for(x=0,n,y=x!+p;if(isprime(y),c++;print1(y",");break)); ) }

Extensions

Definition and offset corrected following a suggestion from Leroy Quet. - Klaus Brockhaus, Mar 02 2010