A364308 - OEIS

%I #20 Oct 01 2024 03:33:18

%S 644,740,804,986,1034,1064,1104,1220,1274,1308,1309,1462,1494,1580,

%T 1748,1884,1885,1924,1988,2013,2014,2108,2134,2254,2288,2294,2330,

%U 2354,2364,2408,2464,2484,2540,2583,2584,2664,2665,2666,2678,2684,2714,2715,2716,2754,2793

%N Numbers k such that k, k+1 and k+2 have exactly 3 distinct prime factors.

%H David A. Corneth, <a href="/A364308/b364308.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1) = A080569(3).

%F {k: A001221(k) = A001221(k+1) = A001221(k+2) = 3}.

%e 644 = 2^2*7*23 has 3 distinct prime factors, 645 = 3*5*43 has 3 distinct prime factors, and 646 = 2*17*19 has 3 distinct prime factors, so 644 is in the sequence.

%t q[n_] := q[n] = PrimeNu[n] == 3; Select[Range[3000], q[#] && q[#+1] && q[#+2] &] (* _Amiram Eldar_, Oct 01 2024 *)

%Y Subsequence of A006073 and of A140077.

%Y Cf. A364307 (2 factors), A364309 (4 factors), A364266 (5 factors), A364265 (6 factors), A001221, A080569.

%K nonn

%O 1,1

%A _R. J. Mathar_, Jul 18 2023