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%I #33 Oct 12 2019 17:31:11
%S 211673,298433,381353,460801,506521,568729,690593,705953,737633,
%T 741305,921529,1056529,1088521,1105553,1141985,1362313,2016721,
%U 2270633,2369809,2535721,2590985,2688833,2956681,2983025,3085201,3112193,3147553,3269161
%N Numbers n such that numbers n through n+6 are the product of exactly three (not necessarily distinct) primes.
%C All terms are == 1 (mod 8). There are no sets of 8 consecutive integers all 3-almost primes.
%C Note that a(1) = A067813(6). - _Michel Marcus_, Nov 24 2015
%H Zak Seidov and Charles R Greathouse IV, <a href="/A259756/b259756.txt">Table of n, a(n) for n = 1..10000</a> (first 4000 from Seidov)
%e 211673=7*11*2749, 211674=2*3*35279, 211675=5*5*8467, 211676=2*2*52919,
%e 211677=3*37*1907, 211678=2*109*971, 211679=13*19*857.
%p W:= numtheory:-bigomega:
%p select(t -> isprime((t+3)/4) and W(t) = 3 and W(t+1) = 3 and W(t+2) = 3
%p and W(t+4) = 3 and W(t+5) = 3 and W(t+6) = 3, [seq(i, i=1..10^7, 8)]); # _Robert Israel_, Nov 24 2015
%t SequencePosition[PrimeOmega[Range[327*10^4]],{3,3,3,3,3,3,3}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 12 2019 *)
%o (PARI) forcomposite(n=1, 4*10^6, if(bigomega(n)==3 && bigomega(n+1)==3 && bigomega(n+2)==3 && bigomega(n+3)==3 && bigomega(n+4)==3 && bigomega(n+5)==3 && bigomega(n+6)==3, print1(n, ", "))) \\ _Altug Alkan_, Nov 08 2015
%o (PARI) {(bo(n)=bigomega(n));n=211673-8;for(i=1,20000,n=n+8;while((a=bo(n))<>3||!isprime((n+3)/4),n=n+8);if(a==bo(n+1)&&
%o a==bo(n+2)&&a==bo(n+4)&&a==bo(n+5)&&a==bo(n+6),print1(n",")))}\\ _Zak Seidov_, Jul 27 2016
%o (PARI) list(lim)=my(v=List(), ct=6, is); forfactored(n=211679, lim\1+6, is=vecsum(n[2][, 2])==3; if(is, if(ct++==7, listput(v, n[1]-6)), ct=0)); Vec(v) \\ _Charles R Greathouse IV_, Jun 26 2019
%Y Subsequence of A259504 and A014612. Cf. A067813.
%K nonn
%O 1,1
%A _Zak Seidov_, Nov 08 2015
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