A198273 Primes not of the form p*q + p + q for any primes p and q.

2, 3, 5, 7, 13, 19, 29, 37, 43, 61, 67, 73, 97, 101, 103, 109, 137, 139, 149, 157, 163, 173, 181, 193, 197, 199, 211, 223, 229, 233, 241, 257, 277, 281, 283, 307, 313, 317, 331, 337, 347, 349, 353, 367, 373, 379, 389, 397, 401, 409, 421, 433, 457, 461, 463

Offset: 1

Author

Reinhard Zumkeller, Oct 23 2011

Keywords

• nonn
• nice

Comments

A067432(A049084(a(n))) = 0; complement of A066938 with respect to A000040.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A049084, A066938, A067432.

Programs

Haskell

a198273 n = a198273_list !! (n-1)
a198273_list = map a000040 $ filter ((== 0) . a067432) [1..]

Mathematica

nn = 500; n2 = PrimePi[nn/3]; Complement[Prime[Range[PrimePi[nn]]], Select[Union[Flatten[Table[(Prime[i] + 1) (Prime[j] + 1) - 1, {i, n2}, {j, n2}]]], # <= nn && PrimeQ[#] &]] (* T. D. Noe, Nov 22 2011 *)
Reap[For[P=2, P<500, P = NextPrime[P], If[Reduce[P == p*q + p + q, {p, q}, Primes] === False, Print[P]; Sow[P]]]][[2, 1]] (* Jean-François Alcover, Dec 10 2015 *)

PARI

do(lim)=my(v=Set(),t);;forprime(p=3,lim,forprime(q=2,p-1,t=p*q+p+q;if(t>lim,break);v=setunion(v,[t])));setminus(primes(primepi(lim)),v) \\ Charles R Greathouse IV, Nov 22 2011