A096788 Numbers m such that both m and m+1 are composite numbers whose sum is a prime of the form 4k+3.

9, 15, 21, 33, 35, 39, 51, 63, 65, 69, 75, 81, 95, 99, 105, 111, 119, 125, 135, 141, 153, 155, 165, 183, 189, 209, 215, 219, 221, 231, 243, 245, 249, 261, 273, 285, 299, 303, 309, 315, 321, 323, 329, 341, 345, 363, 369, 371, 375, 393, 405, 411, 413, 429, 441

Offset: 1

Author

Lekraj Beedassy, Jul 09 2004

Keywords

• nonn

Comments

Odd composite numbers c such that 2*c + 1 is prime. - Alexandre Herrera, Jul 07 2023

Crossrefs

Subsequence (odd numbers) of A096784. See A096787 for the associated primes.

Cf. A060254, A096784, A096785, A096786, A096787, A096676.

Programs

Mathematica

Select[ Range[ 450], PrimeQ[ # ] == PrimeQ[ # + 1] == False && PrimeQ[2# + 1, GaussianIntegers -> True] == True &] (* Robert G. Wilson v, Jul 11 2004 *)

PARI

nextcomposite(k)=if(k<3,4,if(isprime(k),k+1,k));
{m=455;n=4;while(nKlaus Brockhaus, Jul 10 2004

Formula

Equals (A096787 - 1)/2.

Extensions

Corrected and extended by Klaus Brockhaus and Ray Chandler, Jul 10 2000

Incorrect comment about Gaussian primes deleted by N. J. A. Sloane, Mar 02 2011