%I A109611
%S A109611 2,3,5,7,11,13,17,19,23,29,31,37,41,47,53,59,67,71,83,89,101,107,109,
%T A109611 113,127,131,137,139,149,157,167,179,181,191,197,199,211,227,233,239,
%U A109611 251,257,263,269,281,293,307,311,317,337,347,353,359,379,389,401,409
%N A109611 Chen primes: primes p such that p + 2 is either a prime or a semiprime.
%C A109611 43 is the first prime which is not a member (see A102540).
%C A109611 Contains A001359 = lesser of twin primes.
%D A109611 B. Green and T. Tao, Restriction theory of the Selberg sieve, with applications, 
               2005, pp. 5, 14, 18 - 19, 21
%H A109611 R. J. Mathar, <a href="b109611.txt">Table of n, a(n) for n = 1..34076</
               a>
%H A109611 B. Green and T. Tao, <a href="http://arXiv.org/abs/math/0405581">Restriction 
               theory of the Selberg sieve, with applications</a>, arXiv:math/0405581 
               [math.NT]
%H A109611 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ChensTheorem.html">Chen's Theorem</a>
%H A109611 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ChenPrime.html">Chen Prime</a>
%H A109611 Wikipedia, <a href="http://en.wikipedia.org/wiki/Chen_prime">Chen prime</
               a>
%e A109611 a(4) = 7 because 7 + 2 = 9 and 9 is a semiprime.
%e A109611 a(5) = 11 because 11 + 2 = 13, a prime.
%p A109611 with(numtheory): ts_chen:= proc(n) local i, p, ans; ans:=[ ]; for i from 
               1 to n do if ( isprime(i) = true) then if ( isprime(i+2) = true or 
               bigomega(i+2) = 2 ) then ans:=[ op(ans), i ] fi: fi: od: RETURN(ans); 
               end: ts_chen(5000); - Jani Melik (jani_melik(AT)hotmail.com), May 
               04 2006
%p A109611 ts_chen:= proc(n) local i, ans; ans:=[ ]: for i from 1 to n do if ( isprime(i) 
               = 'true') then if ( isprime(i+2) = 'true' or numtheory[bigomega](i+2) 
               = 2) then ans:=[ op(ans), i ] fi fi od: return ans end: ts_chen(1000); 
               - Jani Melik (jani_melik(AT)hotmail.com), May 05 2006
%t A109611 semiPrimeQ[x_] := TrueQ[Plus @@ Last /@ FactorInteger[ x ] == 2]; Select[Prime[Range[100]], 
               PrimeQ[ # + 2] || semiPrimeQ[ # + 2] &] (Delarte)
%o A109611 (PARI) isA001358(n)={ if( bigomega(n)==2, return(1), return(0) ); } isA109611(n)={ 
               if( ! isprime(n), return(0), if( isprime(n+2), return(1), return( 
               isA001358(n+2)) ); ); } { n=1; for(i=1,90000, p=prime(i); if( isA109611(p), 
               print(n," ",p); n++; ); ); } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 20 2006
%Y A109611 Cf. A001358.
%Y A109611 Cf. A112021, A112022, A139689, A139690(n)=a(n)+2.
%Y A109611 Sequence in context: A049555 A052042 A086472 this_sequence A078133 A167773 
               A089189
%Y A109611 Adjacent sequences: A109608 A109609 A109610 this_sequence A109612 A109613 
               A109614
%K A109611 nonn
%O A109611 1,1
%A A109611 Paul Muljadi (paulmuljadi(AT)yahoo.com), Jul 31 2005
%E A109611 Corrected by Alonso Delarte (alonso.delarte(AT)gmail.com), Aug 08 2005
%E A109611 Replaced arxiv URL by non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 07 2009