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A242064 Smallest k such that the union of {A242033(i): 1 <= i <= k} and {A242034(i): 1 <= i <= k} includes all primes {3, ..., prime(n)}.

%I A242064 #12 Aug 21 2014 23:09:51
%S A242064 1,2,9,9,36,36,81,220,220,386,386,386,434,521,896,896,896,1167,1167,
%T A242064 1695,2065,2096,2096,2968,2968,2968,2968,3341,4561,4561,4561,4561,
%U A242064 4672,4672,5964,6203,7158,8294,8294,8294,8740,8740,10452,10452,11075,11075,12092
%N A242064 Smallest k such that the union of {A242033(i): 1 <= i <= k} and {A242034(i): 1 <= i <= k} includes all primes {3, ..., prime(n)}.
%t A242064 lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];(*least prime factor*)
%t A242064 A242033=Map[lpf[#-1]&,Select[Range[6,100000,2],lpf[#-1]<lpf[#-3]&](*A245024*)];
%t A242064 A242034=Map[lpf[#-3]&,Select[Range[6,100000,2],lpf[#-1]>lpf[#-3]&](*A243937*)];
%t A242064 pos={};NestWhile[#+1&,2,(AppendTo[pos,Min[Position[A242033,Prime[#],1,1],Position[A242034,Prime[#],1,1]/.{}->0]];!Last[pos]==0)&];
%t A242064 A242064=Rest[FoldList[Max,-Infinity,Flatten[pos]]] (* _Peter J. C. Moses_, Aug 14 2014 *)
%Y A242064 Cf. A242033, A242034, A242036, A242037.
%K A242064 nonn
%O A242064 2,2
%A A242064 _Vladimir Shevelev_, Aug 13 2014
%E A242064 More terms from _Peter J. C. Moses_, Aug 14 2014