|
%I #9 Mar 27 2020 20:10:28
%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.
%C It is conjectured that if peak/initial value is an integer then it equals 1.
%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.
%K nonn
%O 1,3
%A _Labos Elemer_, Sep 11 2003
|
