A087262 Integer quotient of largest and initial values in 3x+1 iteration, started at n.

1, 1, 5, 1, 3, 2, 7, 1, 5, 1, 4, 1, 3, 3, 10, 1, 3, 2, 4, 1, 3, 2, 6, 1, 3, 1, 341, 1, 3, 5, 297, 1, 3, 1, 4, 1, 3, 2, 7, 1, 225, 1, 4, 1, 3, 3, 196, 1, 3, 1, 4, 1, 3, 170, 167, 1, 3, 1, 5, 2, 3, 148, 146, 1, 3, 1, 4, 1, 3, 2, 130, 1, 126, 1, 4, 1, 3, 3, 10, 1, 3, 112, 111, 1, 3, 2, 6, 1, 3, 1, 101

Offset: 1

Author

Labos Elemer, Sep 11 2003

Keywords

• nonn

Comments

Remarkably often, several consecutive terms are identical or close, showing closeness of peaks too: at n=107-111, a(n)=83-86.

If a(n)=1, then the peak is the start-value (per A166245).

It is conjectured that if peak/initial value is an integer then it equals 1.

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A025586, A056959, A166245 (indices of 1's).

Programs

Mathematica

c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1)c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] Table[Floor[Max[fpl[w]]/w//N], {w, 1, 256}]

Formula

a(n) = floor(A025586(n)/n).