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Search: id:A109611
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| A109611 |
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Chen primes: primes p such that p + 2 is either a prime or a semiprime. |
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+0
45
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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43 is the first prime which is not a member (see A102540).
Contains A001359 = lesser of twin primes.
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REFERENCES
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B. Green and T. Tao, Restriction theory of the Selberg sieve, with applications, 2005, pp. 5, 14, 18 - 19, 21
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LINKS
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R. J. Mathar, Table of n, a(n) for n = 1..34076
B. Green and T. Tao, Restriction theory of the Selberg sieve, with applications
Eric Weisstein's World of Mathematics, Chen's Theorem
Eric Weisstein's World of Mathematics, Chen Prime
Wikipedia, Chen prime
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EXAMPLE
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a(4) = 7 because 7 + 2 = 9 and 9 is a semiprime.
a(5) = 11 because 11 + 2 = 13, a prime.
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MAPLE
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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
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
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MATHEMATICA
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semiPrimeQ[x_] := TrueQ[Plus @@ Last /@ FactorInteger[ x ] == 2]; Select[Prime[Range[100]], PrimeQ[ # + 2] || semiPrimeQ[ # + 2] &] (Delarte)
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PROGRAM
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(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
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CROSSREFS
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Cf. A001358.
Adjacent sequences: A109608 A109609 A109610 this_sequence A109612 A109613 A109614
Sequence in context: A049555 A052042 A086472 this_sequence A078133 A089189 A038612
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KEYWORD
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nonn
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AUTHOR
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Paul Muljadi (paulmuljadi(AT)yahoo.com), Jul 31 2005
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EXTENSIONS
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Corrected by Alonso Delarte (alonso.delarte(AT)gmail.com), Aug 08 2005
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