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A114404 4-almost prime gaps. First differences of A014613.

%I A114404 #15 May 12 2018 17:38:10
%S A114404 8,12,4,14,2,4,21,3,4,2,10,4,22,6,3,1,4,10,2,4,28,5,7,2,6,6,10,5,3,4,
%T A114404 2,14,2,10,16,18,2,1,9,2,7,13,2,10,2,2,4,2,1,13,8,3,1,4,10,24,10,17,3,
%U A114404 15,1,2,10,4,8,4,2,2,3,15,3,3,6,3,7,4,10,4,8,6,4,2,2,8,4,1,35,1,4,7,4,8,6
%N A114404 4-almost prime gaps. First differences of A014613.
%H A114404 T. D. Noe, <a href="/A114404/b114404.txt">Table of n, a(n) for n=1..10000</a>
%F A114404 a(n) = A014613(n+1) - A014613(n).
%e A114404 a(1) = 8 = 24-16 where 16 is the first 4-almost prime and 24 is the second.
%e A114404 a(2) = 12 = 36-24.
%e A114404 a(3) = 4 = 40-36.
%e A114404 a(4) = 14 = 54-40.
%e A114404 a(5) = 2 = 56-54.
%e A114404 a(6) = 4 = 60-56.
%e A114404 a(7) = 21 = 81-60.
%e A114404 a(13) = 22 = 126-104.
%e A114404 a(21) = 28 = 184-156.
%p A114404 A114404 := proc(nmax) local a,i,a014613 ; a := [] ; i := 1 ; a014613 := -1 ; while nops(a) < nmax do if numtheory[bigomega](i) = 4 then if a014613 > 0 then a := [op(a),i-a014613] ; fi ; a014613 := i ; fi ; i := i+1 ; end: a ; end: A114404(200) ; # _R. J. Mathar_, May 10 2007
%t A114404 Differences[Select[Range[800],Total[FactorInteger[#][[All,2]]]==4&]] (* _Harvey P. Dale_, Feb 14 2017 *)
%t A114404 Select[Range[1000],PrimeOmega[#]==4&]//Differences (* _Harvey P. Dale_, May 12 2018 *)
%Y A114404 Cf. A014613, A065516, A111870, A111871, A114403-A114411, A114412-A114422.
%K A114404 easy,nonn
%O A114404 1,1
%A A114404 _Jonathan Vos Post_, Nov 25 2005
%E A114404 Corrected and extended by _R. J. Mathar_, May 10 2007