%I #13 Sep 27 2024 20:57:02

%S 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,

%T 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,

%U 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

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

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

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

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

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

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

%t 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}]

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

%K nonn

%O 1,3

%A _Labos Elemer_, Sep 11 2003