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%I #23 Oct 08 2023 19:28:45
%S 107,263,347,479,863,887,1019,2063,2447,3023,3167,3623,5387,5399,5879,
%T 6599,6983,7079,8423,8699,9743,9887,10463,11807,12263,12347,14207,
%U 15383,15767,18959,20663,22343,23039,23567,24239,27239,32183,33647,33767,37799
%N Numbers m such that m, m-1, m-2 and m-3 are 1,2,3,4-almost primes respectively.
%C Following a suggestion of _Claudio Meller_.
%C m is of the form 12k-1, so m-2 is a multiple of 3 and m-3 is a multiple of 4.
%H Vincenzo Librandi, <a href="/A201220/b201220.txt">Table of n, a(n) for n = 1..1700</a>
%e 6599 is prime, 6598=2*3299 is semiprime, 6597=3*3*733 is 3-almost prime, 6596=2*2*17*97 is 4-almost prime.
%t primeCount[n_] := Plus @@ Transpose[FactorInteger[n]][[2]]; Select[Range[40000], primeCount[#] == 1 && primeCount[#-1] == 2 && primeCount[#-2] == 3 && primeCount[#-3] == 4 &] (* _T. D. Noe_, Nov 28 2011 *)
%t Select[Range[40000],PrimeOmega[Range[#,#+3]]=={4,3,2,1}&]+3 (* _Harvey P. Dale_, Dec 10 2011 *)
%t SequencePosition[PrimeOmega[Range[40000]],{4,3,2,1}][[;;,2]] (* _Harvey P. Dale_, Oct 08 2023 *)
%o (PARI) list(lim)=my(v=List(), L=(lim-2)\3, t); forprime(p=3, L\3, forprime(q=3, min(p, L\p), t=3*p*q+2; if(isprime(t) && isprime((t-1)/2) && bigomega(t-3)==4, listput(v, t)))); Set(v) \\ _Charles R Greathouse IV_, Feb 02 2017
%Y Subsequence of A005385 and of A201147.
%Y Cf. A005383, A112998, A113000, A113008, A072875, A093552.
%K nonn
%O 1,1
%A _Antonio Roldán_, Nov 28 2011
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