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

%I #12 Aug 21 2014 23:09:51

%S 1,2,9,9,36,36,81,220,220,386,386,386,434,521,896,896,896,1167,1167,

%T 1695,2065,2096,2096,2968,2968,2968,2968,3341,4561,4561,4561,4561,

%U 4672,4672,5964,6203,7158,8294,8294,8294,8740,8740,10452,10452,11075,11075,12092

%N 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 lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];(*least prime factor*)

%t A242033=Map[lpf[#-1]&,Select[Range[6,100000,2],lpf[#-1]<lpf[#-3]&](*A245024*)];

%t A242034=Map[lpf[#-3]&,Select[Range[6,100000,2],lpf[#-1]>lpf[#-3]&](*A243937*)];

%t pos={};NestWhile[#+1&,2,(AppendTo[pos,Min[Position[A242033,Prime[#],1,1],Position[A242034,Prime[#],1,1]/.{}->0]];!Last[pos]==0)&];

%t A242064=Rest[FoldList[Max,-Infinity,Flatten[pos]]] (* _Peter J. C. Moses_, Aug 14 2014 *)

%Y Cf. A242033, A242034, A242036, A242037.

%K nonn

%O 2,2

%A _Vladimir Shevelev_, Aug 13 2014

%E More terms from _Peter J. C. Moses_, Aug 14 2014