A189119 - OEIS

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 #12 Jun 24 2021 15:43:04

%S 621,867,891,897,1023,1239,1413,1587,1881,2091,2115,2145,2169,2403,

%T 2451,2505,2601,2769,2871,2889,3003,3129,3171,3231,3237,3243,3399,

%U 3417,3423,3435,3441,3471,3477,3501,3807,3813,3933,3993,4029

%N 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 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 fQ[n_]:=!PrimeQ[n]&&!PrimeQ[n+2]&&!PrimeQ[n+4];

%t lst1=Select[Range[3,9000,2],fQ];

%t lst2=3*Select[Range[3,3000,2],fQ]+6;

%t Intersection[lst1,lst2]

%Y Cf. A002808, A161945.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 16 2011

%E Name clarified by _Tanya Khovanova_, Jun 23 2021