A087974 Largest value of number of distinct prime factors arising in the 3x+1 iteration trajectory started with n.

0, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 3, 3, 3, 1, 2, 3, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3

Offset: 1

Author

Labos Elemer, Sep 25 2003

Keywords

• nonn

Examples

			n=27:iteration-list={27,82,41,124,62,31,....,4,2,1};
A001221 applied to list = L={1,2,1,2,2,...,3,2,2,1,2,2,2,2,2,1,1,1,1,1,0};
a(27)=Max[L]=3 with multiple occurrence.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Programs

Mathematica

fip[x_] := Length[FactorInteger[x]]; c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1); c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1]; lf[x_] := Length[fpl[x]]; pff[x_] := Table[fip[Part[fpl[x], j]], {j, 1, lf[x]}]; Table[Max[pff[w]], {w, 1, 256}]