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Even semiprimes n such that (the largest prime factor of n) + 4 is prime.
2

%I #22 Sep 08 2022 08:45:48

%S 6,14,26,38,74,86,134,158,194,206,218,254,326,386,446,458,554,614,626,

%T 698,758,794,878,914,926,974,998,1226,1286,1346,1478,1514,1538,1646,

%U 1706,1718,1754,1766,1814,1874,1934,2018,2174,2186,2426,2558,2594,2606

%N Even semiprimes n such that (the largest prime factor of n) + 4 is prime.

%C Also numbers n of the form 2p such that p and p+4 are prime.

%C n is congruent to 2 modulo 3 for n > 6.

%H Harvey P. Dale, <a href="/A165986/b165986.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 2*A023200(n). - _R. J. Mathar_, Jun 23 2011

%t Select[Range[2,3000,2],PrimeOmega[#]==2&&PrimeQ[FactorInteger[#][[-1,1]]+4]&] (* _Harvey P. Dale_, Mar 09 2021 *)

%o (Magma) [ 2*p: p in PrimesUpTo(1500) | IsPrime(p+4) ]; // _Klaus Brockhaus_, Jun 26 2011

%o (PARI) forprime(p=2,1e3,if(isprime(p+4),print1(p+p", "))) \\ _Charles R Greathouse IV_, Jun 26 2011

%K nonn,easy

%O 1,1

%A _Giovanni Teofilatto_, Oct 03 2009, Jun 26 2011

%E Definition clarified by _Harvey P. Dale_, Jul 14 2021