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A364266 The first term in a chain of at least 3 consecutive numbers each with exactly 5 distinct prime factors.

%I A364266 #22 Oct 01 2024 03:33:10
%S A364266 1042404,3460280,3818828,3998664,4638984,4991964,5540248,5701254,
%T A364266 5715500,5964958,6772050,6794084,7237384,7453964,7459088,7745318,
%U A364266 7757034,7993194,8083634,8153430,8168194,8273628,8340834,8340980,8414756,8486994,8698898,8722634,8758904
%N A364266 The first term in a chain of at least 3 consecutive numbers each with exactly 5 distinct prime factors.
%H A364266 David A. Corneth, <a href="/A364266/b364266.txt">Table of n, a(n) for n = 1..10000</a>
%F A364266 a(1) = A087978(3).
%F A364266 {k: A001221(k) = A001221(k+1) = A001221(k+2) = 5}. - _R. J. Mathar_, Jul 18 2023
%e A364266 1042404 = 2^2*3*11*53*149, 1042405 = 5*6*143*29*79 and 1042406 = 2*17*23*31*43 each have 5 distinct prime factors, so 1042404 is in the sequence.
%p A364266 omega := proc(n)
%p A364266     nops(numtheory[factorset](n)) ;
%p A364266 end proc:
%p A364266 for k from 1 do
%p A364266     if omega(k) = 5 then
%p A364266         if omega(k+1) = 5 then
%p A364266             if omega(k+2) = 5 then
%p A364266                 print(k) ;
%p A364266             end if;
%p A364266         end if;
%p A364266     end if;
%p A364266 end do:
%t A364266 seq[lim_] := Module[{s  = {}, q1 = False, q2 = False, q3}, Do[q3 = PrimeNu[k] == 5; If[q1 && q2 && q3, AppendTo[s, k-2]]; q1 = q2; q2 = q3, {k, 3, lim}]; s]; seq[10^7] (* _Amiram Eldar_, Oct 01 2024 *)
%Y A364266 Cf. A192203 (subsequence for squarefree triples). Subsequence of A140079 (2 consec.) and of A006073.
%Y A364266 Cf. A364308 (3 dist. factors), A364309 (4 dist. factors), A364265 (6 dist. factors), A001221, A087978.
%K A364266 nonn
%O A364266 1,1
%A A364266 _R. J. Mathar_, Jul 16 2023