This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A109611 Chen primes: primes p such that p + 2 is either a prime or a semiprime. 70
 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 43 is the first prime which is not a member (see A102540). Contains A001359 = lesser of twin primes. A063637 is a subsequence. - Reinhard Zumkeller, Mar 22 2010 In 1966 Chen proved that this sequence is infinite; his proof did not appear until 1973 due to the Cultural Revolution. - Charles R Greathouse IV, Jul 12 2016 LINKS R. J. Mathar, Table of n, a(n) for n = 1..34076 Jing Run Chen, On the representation of a larger even integer as the sum of a prime and the product of at most two primes, Sci. Sinica 16 (1973), pp. 157-176. B. Green and T. Tao, Restriction theory of the Selberg sieve, with applications, arXiv:math/0405581 [math.NT], 2004-2005, pp. 5, 14, 18-19, 21. B. Green and T. Tao, Restriction theory of the Selberg sieve, with applications, J. Théor. Nombres Bordeaux 18, 2006. Eric Weisstein's World of Mathematics, Chen's Theorem Eric Weisstein's World of Mathematics, Chen Prime Wikipedia, Chen prime FORMULA a(n)+2 = A139690(n). EXAMPLE a(4) = 7 because 7 + 2 = 9 and 9 is a semiprime. a(5) = 11 because 11 + 2 = 13, a prime. MAPLE A109611 := proc(n)     option remember;     if n =1 then         2;     else         a := nextprime(procname(n-1)) ;         while true do             if isprime(a+2) or numtheory[bigomega](a+2) = 2 then                 return a;             end if;             a := nextprime(a) ;         end do:     end if; end proc: # R. J. Mathar, Apr 26 2013 MATHEMATICA semiPrimeQ[x_] := TrueQ[Plus @@ Last /@ FactorInteger[ x ] == 2]; Select[Prime[Range], PrimeQ[ # + 2] || semiPrimeQ[ # + 2] &] (* Alonso del Arte, Aug 08 2005 *) SequencePosition[PrimeOmega[Range], {1, _, 1|2}][[All, 1]] (* Jean-François Alcover, Feb 10 2018 *) PROG (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, Aug 20 2006 (PARI) list(lim)=my(v=List(), semi=List(), L=lim+2, p=3); forprime(q=3, L\3, forprime(r=3, min(L\q, q), listput(semi, q*r))); semi=Set(semi); forprime(q=7, lim, if(setsearch(semi, q+2), listput(v, q))); forprime(q=5, L, if(q-p==2, listput(v, p)); p=q); Set(v) \\ Charles R Greathouse IV, Aug 25 2017 CROSSREFS Cf. A001358, A112021, A112022, A139689, A269256. Sequence in context: A245576 A086472 A219669 * A181325 A078133 A268513 Adjacent sequences:  A109608 A109609 A109610 * A109612 A109613 A109614 KEYWORD nonn AUTHOR Paul Muljadi, Jul 31 2005 EXTENSIONS Corrected by Alonso del Arte, Aug 08 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 22 13:35 EDT 2019. Contains 328318 sequences. (Running on oeis4.)