A096787 Primes of form 4n+3 that are the sum of two consecutive composite numbers.

19, 31, 43, 67, 71, 79, 103, 127, 131, 139, 151, 163, 191, 199, 211, 223, 239, 251, 271, 283, 307, 311, 331, 367, 379, 419, 431, 439, 443, 463, 487, 491, 499, 523, 547, 571, 599, 607, 619, 631, 643, 647, 659, 683, 691, 727, 739, 743, 751, 787, 811, 823, 827

Offset: 1

Author

Lekraj Beedassy, Jul 09 2004

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A060254. See A096788 for values 2n+1. See A096676 for n values.

Cf. A060254, A096784, A096785, A096786, A096788, A096676, A096679.

Programs

Mathematica

2Select[ Range[ 450], PrimeQ[ # ] == PrimeQ[ # + 1] == False && PrimeQ[2# + 1, GaussianIntegers -> True] == True &] + 1 (* Robert G. Wilson v, Jul 11 2004 *)
Select[Total/@Partition[Select[Range[500],CompositeQ],2,1],PrimeQ[#] && IntegerQ[ (#-3)/4]&] (* Harvey P. Dale, Mar 06 2019 *)

PARI

nextcomposite(k)=if(k<3,4,if(isprime(k),k+1,k));
{m=440;n=4;while(nKlaus Brockhaus, Jul 10 2004

Formula

Equals 1+2*A096788.

Extensions

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