cp's OEIS Frontend

A375239 Numbers k such that k, k+1, ..., k+5 all have 3 prime factors (counted with multiplicity).

%I A375239 #19 Aug 17 2024 23:09:24
%S A375239 2522,4921,18241,25553,27290,40313,90834,95513,98282,98705,117002,
%T A375239 120962,136073,136865,148682,153794,181441,181554,185825,211673,
%U A375239 211674,212401,215034,216361,231002,231665,234641,236041,236634,266282,281402,285410,298433,298434,330473,331985,346505,381353
%N A375239 Numbers k such that k, k+1, ..., k+5 all have 3 prime factors (counted with multiplicity).
%C A375239 First differs from A045942 at position 20, where a(20) = 211673 but A045942(20) = 204323.
%C A375239 All terms == 1 or 2 (mod 8).
%C A375239 One of the numbers k, k+1, ..., k+5 is a Zumkeller number (A083207), since it is of the form 2*3*p, where p is prime > 3. - _Ivan N. Ianakiev_, Aug 08 2024
%H A375239 Robert Israel, <a href="/A375239/b375239.txt">Table of n, a(n) for n = 1..10000</a>
%e A375239 a(3) = 18241 is a term because
%e A375239   18241 = 17 * 29 * 37
%e A375239   18242 =  2 * 7 * 1303
%e A375239   18243 =  3^2 * 2027
%e A375239   18244 =  2^2 * 4561
%e A375239   18245 =  5 * 41 * 89
%e A375239   18246 =  2 * 3 * 3041
%e A375239 are all products of 3 primes (counted with multiplicity).
%p A375239 R:= NULL: count:= 0: p:= 1:
%p A375239 while count < 100 do
%p A375239   p:= nextprime(p);
%p A375239   x:= 4*p;
%p A375239   if andmap(t -> numtheory:-bigomega(t)=3, [x-2,x-1,x+1,x+2]) then
%p A375239     if numtheory:-bigomega(x-3) = 3 then R:= R, x-3; count:= count+1;  fi;
%p A375239     if numtheory:-bigomega(x+3) = 3 then R:= R, x-2; count:= count+1;  fi;
%p A375239   fi;
%p A375239 od:
%p A375239 R;
%t A375239 s = {}; Do[If[{3, 3, 3, 3, 3, 3} == PrimeOmega[Range[k, k + 5]],
%t A375239 AppendTo[s, k]], {k, 1000000}]; s
%Y A375239 Subsequence of A045942 and of A113789. Contains A259756.
%K A375239 nonn
%O A375239 1,1
%A A375239 _Zak Seidov_ and _Robert Israel_, Aug 06 2024