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

3,1

Links

Table of n, a(n) for n=3..54.

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]<lpf3[#-3]&](*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 *)

Crossrefs

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

Sequence in context: A336785 A080739 A361665 * A056424 A050324 A211227

Adjacent sequences: A242062 A242063 A242064 * A242066 A242067 A242068

Keyword

nonn

Author

Vladimir Shevelev, Aug 13 2014

Extensions

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

Status

approved