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

1,1

Comments

Green & Tao prove that this sequence is infinite.

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.

Example

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.

Prog

(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

Crossrefs

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

Cf. A291525.

Sequence in context: A117743 A216495 A034849 * A106070 A346991 A038880

Adjacent sequences: A269253 A269254 A269255 * A269257 A269258 A269259

Keyword

nonn

Author

Charles R Greathouse IV, Jul 12 2016

Status

approved