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

1,3

Links

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

Example

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.

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}]

Crossrefs

Sequence in context: A353656 A196062 A283682 * A008679 A029435 A089643

Adjacent sequences: A087971 A087972 A087973 * A087975 A087976 A087977

Keyword

nonn

Author

Labos Elemer, Sep 25 2003

Status

approved