A117244 - OEIS

%I #14 Oct 19 2021 21:32:48

%S 79,97,163,173,223,277,331,367,373,383,397,439,457,547,593,607,613,

%T 673,691,709,727,733,739,757,773,853,907,929,967,997,1013,1069,1087,

%U 1103,1123,1129,1171,1181,1213,1223,1237,1249,1307,1373,1423,1433,1447,1493

%N Single (or isolated or non-twin) primes (A007510) that are not Chen primes (A109611).

%H Amiram Eldar, <a href="/A117244/b117244.txt">Table of n, a(n) for n = 1..10000</a>

%e 79 is single prime, but not Chen prime, since 79 -2 = 77 = 7*11 is composite, and 79 + 2 = 81 = 3^4 is neither prime nor semiprime.

%p isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc: isA109611 := proc(n) if isprime(n) then isprime(n+2) or isA001358(n+2) ; else false; end if; end proc: isA007510 := proc(n) if isprime(n) then not isprime(n-2) and not isprime(n+2) ; else false; end if ; end proc: isA117244 := proc(n) isA007510(n) and not isA109611(n) ; end proc: for n from 1 to 4000 do if isA117244(n) then printf("%d,",n) ; fi; end do ; # _R. J. Mathar_, Dec 09 2009

%t Select[Range[1500], PrimeQ[#] && !PrimeQ[#-2] && PrimeOmega[#+2] > 2 &] (* _Amiram Eldar_, Oct 19 2021 *)

%o (PARI) isok(p) = isprime(p) && !isprime(p-2) && !isprime(p+2) && (bigomega(p+2) > 2); \\ _Michel Marcus_, Oct 19 2021

%Y Cf. A007510, A109611.

%K nonn

%O 1,1

%A _Jani Melik_, Apr 22 2006

%E Terms beyond 397 from _R. J. Mathar_, Dec 09 2009

%E Offset corrected by _Amiram Eldar_, Oct 19 2021