A269256 Chen primes p such that there are Chen primes p > q > r in arithmetic progression.

7, 11, 17, 19, 23, 29, 31, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 113, 127, 131, 137, 139, 149, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 347

Offset: 1

Author

Charles R Greathouse IV, Jul 12 2016

Keywords

• nonn

Comments

Green & Tao prove that this sequence is infinite.

Examples

			19 is in the sequence since 3 < 11 < 19, 19 - 11 = 11 - 3, all three are prime, and 3+2, 11+2, and 19+2 are each either prime or semiprime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Ben Green and Terence Tao, Restriction theory of the Selberg sieve, with applications, Journal de théorie des nombres de Bordeaux 18:1 (2006), pp. 147-182.

Crossrefs

Subsequence of A109611. This is the Chen prime analog of A216495.

Cf. A291525.

Programs

PARI

issemi(n)=bigomega(n)==2
ischen(n)=isprime(n) && (isprime(n+2) || issemi(n+2))
is(n)=if(!ischen(n), return(0)); forprime(p=2,n-4, if((p+n)%4==2 && ischen(p) && ischen((p+n)/2), return(1))); 0