A117242 Chen primes that are not twin primes.
2, 23, 37, 47, 53, 67, 83, 89, 113, 127, 131, 157, 167, 211, 233, 251, 257, 263, 293, 307, 317, 337, 353, 359, 379, 389, 401, 409, 443, 449, 467, 479, 487, 491, 499, 503, 509, 541, 557, 563, 577, 587, 631, 647, 653, 677, 683, 701, 719, 743, 751, 761, 769, 787, 797, 839, 863, 877, 887, 911, 919, 937, 941, 947, 953, 971, 977, 983, 991
Offset: 1
Keywords
Examples
a(1) = 2, 2 is a Chen prime but is not in a twin prime pair. a(2) = 23 is a Chen prime, but is not in a twin prime pair.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Maple
ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then RETURN('true') else RETURN('false') fi fi end: ts_chen_non_twin_primes:=proc(n) local i, ans; ans:=[ ]: for i from 1 to n do if (ischenprime(i) = 'true') and (isprime(i+2) = 'false' and isprime(i-2) = 'false') then ans:=[op(ans), i]: fi od; RETURN(ans) end: ts_chen_non_twin_primes(1000); -
Mathematica
Lim=PrimePi[1000];Select[Select[Prime[Range[Lim]],PrimeOmega[#+2]<3&],!MemberQ[Select[ Prime[ Range[Lim]], PrimeQ[ # - 2]||PrimeQ[#+2]&] ,#]&] (* James C. McMahon, Sep 27 2024 *)
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PARI
is(n)=isprime(n)&&bigomega(n+2)==2&&!isprime(n-2) \\ Charles R Greathouse IV, May 04 2013