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

1,3

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

Table of n, a(n) for n=1..91.

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

Formula

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

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}]

Crossrefs

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

Sequence in context: A068237 A373363 A083345 * A082343 A166125 A199074

Adjacent sequences: A087259 A087260 A087261 * A087263 A087264 A087265

Keyword

nonn

Author

Labos Elemer, Sep 11 2003

Status

approved