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A242065 Smallest k such that the union of {A242059(i): 1 <= i <= k} and {A242060(i): 1 <= i <= k} includes all primes {5, ..., prime(n)}.

%I A242065 #12 Aug 21 2014 23:08:23
%S A242065 2,3,4,8,8,17,17,17,60,60,60,60,60,60,60,60,60,60,179,179,179,179,179,
%T A242065 179,179,179,264,264,264,319,319,319,319,365,1112,1112,1112,1112,1112,
%U A242065 1112,1112,1112,1112,1112,1112,4372,4372,4372,4372,4372,15504,15504
%N A242065 Smallest k such that the union of {A242059(i): 1 <= i <= k} and {A242060(i): 1 <= i <= k} includes all primes {5, ..., prime(n)}.
%t A242065 lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];(*least prime factor*)
%t A242065 lpf3[n_]:=lpf3[n]=If[#==1,1,lpf[#]]&[n/3^IntegerExponent[n,3]];
%t A242065 A242059=Map[lpf3[#-1]&,Select[Range[4,100000,2],lpf3[#-1]<lpf3[#-3]&](*A242057*)];
%t A242065 A242060=Map[lpf3[#-3]&,Select[Range[4,100000,2],lpf3[#-1]>lpf3[#-3]&](*A242058*)];
%t A242065 pos={};NestWhile[#+1&,3,(AppendTo[pos,Min[Position[A242059,Prime[#],1,1],Position[A242060,Prime[#],1,1]/.{}->0]];!Last[pos]==0)&];
%t A242065 A242065=Rest[FoldList[Max,-Infinity,Flatten[pos]]] (* _Peter J. C. Moses_, Aug 14 2014 *)
%Y A242065 Cf. A242033, A242034, A242036, A242037, A242057, A242058, A242059, A242060, A242064.
%K A242065 nonn
%O A242065 3,1
%A A242065 _Vladimir Shevelev_, Aug 13 2014
%E A242065 More terms from _Peter J. C. Moses_, Aug 14 2014