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

1,1

Links

Table of n, a(n) for n=1..59.

Formula

Equals (A060254 -1)/2.

Mathematica

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

Prog

(PARI) nextcomposite(k)=if(k<3, 4, if(isprime(k), k+1, k));
{m=230; n=4; while(n<m, k=nextcomposite(n+1); p=n+k; if(k==n+1&&isprime(p), print1(n, ", ")); n=k)} \\ Klaus Brockhaus, Jul 11 2004
(Magma)[n: n in [0..250]|not IsPrime(n) and not IsPrime(n+1) and IsPrime(2*n+1)] // Vincenzo Librandi, Dec 18 2010

Crossrefs

See A060254 for the primes 2n+1.

Cf. A096785, A096786, A096787, A096788.

Sequence in context: A299143 A068780 A174041 * A175859 A059869 A327863

Adjacent sequences: A096781 A096782 A096783 * A096785 A096786 A096787

Keyword

nonn

Author

Lekraj Beedassy, Jul 09 2004

Extensions

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

Status

approved