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)}.

2, 3, 4, 8, 8, 17, 17, 17, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 179, 179, 179, 179, 179, 179, 179, 179, 264, 264, 264, 319, 319, 319, 319, 365, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 4372, 4372, 4372, 4372, 4372, 15504, 15504

Offset: 3

Author

Vladimir Shevelev, Aug 13 2014

Keywords

• nonn

Crossrefs

Cf. A242033, A242034, A242036, A242037, A242057, A242058, A242059, A242060, A242064.

Programs

Mathematica

lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];(*least prime factor*)
lpf3[n_]:=lpf3[n]=If[#==1,1,lpf[#]]&[n/3^IntegerExponent[n,3]];
A242059=Map[lpf3[#-1]&,Select[Range[4,100000,2],lpf3[#-1]A242057*)];
A242060=Map[lpf3[#-3]&,Select[Range[4,100000,2],lpf3[#-1]>lpf3[#-3]&](*A242058*)];
pos={};NestWhile[#+1&,3,(AppendTo[pos,Min[Position[A242059,Prime[#],1,1],Position[A242060,Prime[#],1,1]/.{}->0]];!Last[pos]==0)&];
A242065=Rest[FoldList[Max,-Infinity,Flatten[pos]]] (* Peter J. C. Moses, Aug 14 2014 *)

Extensions

More terms from Peter J. C. Moses, Aug 14 2014