A096784 Numbers n such that both n and n+1 are composite numbers that sum up to a prime.

8, 9, 14, 15, 20, 21, 26, 33, 35, 39, 44, 48, 50, 51, 54, 56, 63, 65, 68, 69, 74, 75, 81, 86, 90, 95, 98, 99, 105, 111, 114, 116, 119, 120, 125, 128, 134, 135, 140, 141, 146, 153, 155, 158, 165, 168, 174, 176, 183, 186, 189, 194, 200, 204, 209, 215, 216, 219, 221

Offset: 1

Author

Lekraj Beedassy, Jul 09 2004

Keywords

• nonn

Crossrefs

See A060254 for the primes 2n+1.

Cf. A096785, A096786, A096787, A096788.

Programs

Magma

[n: n in [0..250]|not IsPrime(n) and not IsPrime(n+1) and IsPrime(2*n+1)] // Vincenzo Librandi, Dec 18 2010

Mathematica

Select[ Range[ 225], PrimeQ[ # ] == PrimeQ[ # + 1] == False && PrimeQ[2# + 1] == True &] (* Robert G. Wilson v, Jul 11 2004 *)

PARI

nextcomposite(k)=if(k<3,4,if(isprime(k),k+1,k));
{m=230;n=4;while(nKlaus Brockhaus, Jul 11 2004

Formula

Equals (A060254 -1)/2.

Extensions

Corrected and extended by Klaus Brockhaus and Ray Chandler, Jul 10 2004