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A364308
Numbers k such that k, k+1 and k+2 have exactly 3 distinct prime factors.
5
644, 740, 804, 986, 1034, 1064, 1104, 1220, 1274, 1308, 1309, 1462, 1494, 1580, 1748, 1884, 1885, 1924, 1988, 2013, 2014, 2108, 2134, 2254, 2288, 2294, 2330, 2354, 2364, 2408, 2464, 2484, 2540, 2583, 2584, 2664, 2665, 2666, 2678, 2684, 2714, 2715, 2716, 2754, 2793
OFFSET
1,1
LINKS
FORMULA
a(1) = A080569(3).
{k: A001221(k) = A001221(k+1) = A001221(k+2) = 3}.
EXAMPLE
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.
MATHEMATICA
q[n_] := q[n] = PrimeNu[n] == 3; Select[Range[3000], q[#] && q[#+1] && q[#+2] &] (* Amiram Eldar, Oct 01 2024 *)
CROSSREFS
Subsequence of A006073 and of A140077.
Cf. A364307 (2 factors), A364309 (4 factors), A364266 (5 factors), A364265 (6 factors), A001221, A080569.
Sequence in context: A061324 A089295 A195808 * A260838 A304607 A168626
KEYWORD
nonn
AUTHOR
R. J. Mathar, Jul 18 2023
STATUS
approved