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A241817 Semiprimes sp such that sp-3 is prime.

%I A241817 #14 Oct 14 2018 12:17:06
%S A241817 6,10,14,22,26,34,46,62,74,82,86,106,134,142,166,194,202,214,226,254,
%T A241817 274,314,334,362,382,386,422,446,466,482,502,526,566,622,634,662,694,
%U A241817 746,842,862,866,886,914,922,974,1042,1094,1126,1154,1174,1226,1234,1262
%N A241817 Semiprimes sp such that sp-3 is prime.
%C A241817 Even numbers of the form 2p, p prime, that can be expressed as the sum of two primes in at least two ways as 2p = p + p = 3 + (2p-3). For example, 34 is in the sequence because 34 = 2*17 = 17 + 17 = 3 + 31. These are the only numbers that have Goldbach partitions with both a minimum and a maximum possible difference between their prime parts, i.e., |p-p| = 0 and |(2p-3)-3| = 2p-6 respectively. - _Wesley Ivan Hurt_, Apr 08 2018
%H A241817 K. D. Bajpai, <a href="/A241817/b241817.txt">Table of n, a(n) for n = 1..2500</a>
%F A241817 a(n) = 2 * A063908(n). - _Wesley Ivan Hurt_, Apr 08 2018
%e A241817 a(2) = 10 = 2*5, which is semiprime and 10-3 = 7 is a prime.
%e A241817 a(6) = 34 = 2*17, which is semiprime and 34-3 = 31 is a prime.
%p A241817 with(numtheory): A241817:= proc(); if bigomega(x)=2 and isprime(x-3) then  RETURN (x); fi; end: seq(A241817 (), x=1..3000);
%t A241817 2 Select [Prime[Range[5!]], PrimeQ[2 # - 3] &] (* _Vincenzo Librandi_, Apr 10 2018 *)
%t A241817 Select[Range[1500],PrimeOmega[#]==2&&PrimeQ[#-3]&] (* _Harvey P. Dale_, Oct 14 2018 *)
%Y A241817 Cf. A001358, A063908, A092207, A123017, A198327.
%K A241817 nonn
%O A241817 1,1
%A A241817 _K. D. Bajpai_, Apr 29 2014