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A189119 Sums k of three consecutive odd numbers, all of which are composite, such that k is also the smallest in a set of three consecutive odd numbers, all of which are composite.

%I A189119 #12 Jun 24 2021 15:43:04
%S A189119 621,867,891,897,1023,1239,1413,1587,1881,2091,2115,2145,2169,2403,
%T A189119 2451,2505,2601,2769,2871,2889,3003,3129,3171,3231,3237,3243,3399,
%U A189119 3417,3423,3435,3441,3471,3477,3501,3807,3813,3933,3993,4029
%N A189119 Sums k of three consecutive odd numbers, all of which are composite, such that k is also the smallest in a set of three consecutive odd numbers, all of which are composite.
%e A189119 621 is a term: it is the smallest of three consecutive odd composite numbers (621 = 3^3*23, 623 = 7*89, 625 = 5^4) and is also the sum of three consecutive odd composite numbers (205 = 5*41, 207 = 3^2*23, 209 = 11*19, and 205 + 207 + 209 = 621).
%t A189119 fQ[n_]:=!PrimeQ[n]&&!PrimeQ[n+2]&&!PrimeQ[n+4];
%t A189119 lst1=Select[Range[3,9000,2],fQ];
%t A189119 lst2=3*Select[Range[3,3000,2],fQ]+6;
%t A189119 Intersection[lst1,lst2]
%Y A189119 Cf. A002808, A161945.
%K A189119 nonn
%O A189119 1,1
%A A189119 _Vladimir Joseph Stephan Orlovsky_, Apr 16 2011
%E A189119 Name clarified by _Tanya Khovanova_, Jun 23 2021