login
A096788
Numbers m such that both m and m+1 are composite numbers whose sum is a prime of the form 4k+3.
10
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 that 2*c + 1 is prime. - Alexandre Herrera, Jul 07 2023
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.
Sequence in context: A007962 A061254 A175626 * A050991 A033553 A020192
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