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%I #19 Dec 19 2022 10:19:02
%S 9,15,27,33,57,63,75,93,105,135,153,177,195,237,267,273,363,393,405,
%T 435,453,483,495,567,573,597,603,657,687,705,723,747,765,825,915,933,
%U 987,1017,1035,1065,1113,1167,1197,1227,1233,1287,1293,1323,1377,1443,1455,1485
%N Composite numbers n such that n+4 and n-4 are both prime.
%C Composite numbers of the form A023202(k)+4, any k.
%C A087680 without the {7} [Proof: there are no 3 primes in arithmetic progression p, p+4, p+8, except p=3].
%C A164383 INTERSECT A164384; A087680 INTERSECT A002808.
%C If p=3*l+1, p+8 were divisible by 3, and if p=3*l+2, p+4 were divisible by 3. - _R. J. Mathar_, Aug 20 2009]
%C All terms are divisible by 3. - _Zak Seidov_, Apr 22 2015
%F a(n) = A023202(n+1)+4 = A087680(n+1). - _Zak Seidov_, Apr 22 2015
%e a(1) = 5(prime)+4 = 13(prime)-4 = 9 (composite).
%e a(2) = 11(prime)+4 = 19(prime)-4 = 15 (composite).
%t Select[Range[8, 2000], PrimeQ[#+4] && PrimeQ[#-4] &] (* _Vincenzo Librandi_, Apr 22 2015 *)
%o (Magma) [n: n in [8..2000] | IsPrime(n+4) and IsPrime(n-4)]; // _Vincenzo Librandi_, Apr 22 2015
%Y Cf. A002808, A023202, A087680.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Aug 14 2009
%E 65 removed, 337 changed to 237 etc. by _R. J. Mathar_, Aug 20 2009
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