A096788 Numbers n such that both n and n+1 are composite numbers that add up to 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

1,1

Comments

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

Links

Table of n, a(n) for n=1..55.

Formula

Equals (A096787 -1 )/2.

Mathematica

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

Prog

(PARI) nextcomposite(k)=if(k<3, 4, if(isprime(k), k+1, k));
{m=455; n=4; while(n<m, k=nextcomposite(n+1); p=n+k; if(isprime(p)&&(p%4)==3, print1(n, ", ")); n=k)} \\ Klaus Brockhaus, Jul 10 2004

Crossrefs

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

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

Sequence in context: A007962 A061254 A175626 * A050991 A033553 A020192

Adjacent sequences: A096785 A096786 A096787 * A096789 A096790 A096791

Keyword

nonn

Author

Lekraj Beedassy, Jul 09 2004

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

Status

approved