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)}.

1, 2, 9, 9, 36, 36, 81, 220, 220, 386, 386, 386, 434, 521, 896, 896, 896, 1167, 1167, 1695, 2065, 2096, 2096, 2968, 2968, 2968, 2968, 3341, 4561, 4561, 4561, 4561, 4672, 4672, 5964, 6203, 7158, 8294, 8294, 8294, 8740, 8740, 10452, 10452, 11075, 11075, 12092

Offset: 2

Author

Vladimir Shevelev, Aug 13 2014

Keywords

• nonn

Crossrefs

Cf. A242033, A242034, A242036, A242037.

Programs

Mathematica

lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];(*least prime factor*)
A242033=Map[lpf[#-1]&,Select[Range[6,100000,2],lpf[#-1]A245024*)];
A242034=Map[lpf[#-3]&,Select[Range[6,100000,2],lpf[#-1]>lpf[#-3]&](*A243937*)];
pos={};NestWhile[#+1&,2,(AppendTo[pos,Min[Position[A242033,Prime[#],1,1],Position[A242034,Prime[#],1,1]/.{}->0]];!Last[pos]==0)&];
A242064=Rest[FoldList[Max,-Infinity,Flatten[pos]]] (* Peter J. C. Moses, Aug 14 2014 *)

Extensions

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