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A127171 Difference between largest prime factors of two successive 3-almost primes.

%I A127171 #10 Aug 12 2015 21:14:49
%S A127171 1,0,2,-2,4,-2,2,4,-6,0,8,-6,4,6,-10,-2,14,-6,10,-16,4,6,-10,4,8,10,
%T A127171 -16,18,-26,8,10,-16,30,-20,-6,30,-30,6,2,24,-14,-22,6,18,16,-28,-6,
%U A127171 10,30,-16,-14,-12,48,-42,-6,50,-54,34,-24,26,-14,-10,48,-54,-2,20,16,24,-52,-6,16,44,-42,48,-26,-30,-10,70,-46,-24,-6,16
%N A127171 Difference between largest prime factors of two successive 3-almost primes.
%F A127171 a(n) = A006530(A014612(n+1)) - A006530(A014612(n)).
%e A127171 a(1) = 1 because 3-almostprime(1) = 8 and 3-almostprime(2) = 12, greatest prime factor(12) = 3, greatest prime factor(8) = 2 and 3-2 = 1.
%e A127171 a(3) = gpf(20) - gpf(18) = 5 - 3 = 2.
%e A127171 a(4) = gpf(27) - gpf(20) = 3 - 5 = -2.
%p A127171 A014612 := proc(nmax) local a,n; a := [8] ; while nops(a) < nmax do n := op(-1,a)+1 ; while numtheory[bigomega](n) <> 3 do n := n+1 ; od ; a := [op(a),n] ; od ; RETURN(a) ; end: A006530 := proc(n) op(1,op(-1,ifactors(n)[2])) ; end: A127171 := proc(nmax) local a,threeAlm,i ; threeAlm := A014612(nmax) ; a := [] ; for i from 2 to nops(threeAlm) do a := [op(a), A006530(op(i,threeAlm))-A006530(op(i-1,threeAlm)) ] ; od ; RETURN(a) ; end: A127171(100) ; # _R. J. Mathar_, Apr 01 2007
%t A127171 Last[#]-First[#]&/@(Partition[FactorInteger[#][[-1,1]]&/@Select[Range[ 500],PrimeOmega[#]==3&],2,1]) (* _Harvey P. Dale_, May 30 2014 *)
%Y A127171 Cf. A014612, A126663.
%K A127171 easy,sign
%O A127171 1,3
%A A127171 _Jonathan Vos Post_, Mar 25 2007
%E A127171 More terms from _R. J. Mathar_, Apr 01 2007