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

1,1

Links

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

Formula

Equals 1+2*A096788.

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 *)

Prog

(PARI) nextcomposite(k)=if(k<3, 4, if(isprime(k), k+1, k));
{m=440; n=4; while(n<m, k=nextcomposite(n+1); p=n+k; if(isprime(p)&&(p%4)==3, print1(p, ", ")); n=k)} \\ Klaus Brockhaus, Jul 10 2004

Crossrefs

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

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

Sequence in context: A043298 A286313 A040068 * A104006 A117065 A006035

Adjacent sequences: A096784 A096785 A096786 * A096788 A096789 A096790

Keyword

nonn

Author

Lekraj Beedassy, Jul 09 2004

Extensions

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

Status

approved