A364308 Numbers k such that k, k+1 and k+2 have exactly 3 distinct prime factors.

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

David A. Corneth, Table of n, a(n) for n = 1..10000

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 *)
SequencePosition[PrimeNu[Range[3000]], {3, 3, 3}][[;; , 1]] (* Harvey P. Dale, Jul 16 2026 *)

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: A089295 A195808 A381621 * A260838 A304607 A168626

Adjacent sequences: A364305 A364306 A364307 * A364309 A364310 A364311

Keyword

nonn,changed

Author

R. J. Mathar, Jul 18 2023

Status

approved