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A269256 Chen primes p such that there are Chen primes p > q > r in arithmetic progression. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A038880 A019365

Adjacent sequences:  A269253 A269254 A269255 * A269257 A269258 A269259

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Jul 12 2016

STATUS

approved

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Last modified March 19 00:15 EDT 2019. Contains 321306 sequences. (Running on oeis4.)