|
|
A095388
|
|
Smallest initial value for 3x+1 trajectory, divisible by 2^n, such that emerging peak-value exceeds this start-value.
|
|
0
|
|
|
6, 12, 120, 432, 864, 1728, 3456, 6912, 931328, 4357120, 19789824, 249753600, 499507200, 1272561664, 5226070016, 10452140032, 351882051584, 1215818366976, 3364158439424, 6953815244800, 13907630489600, 27815260979200, 55630521958400, 1343005923475456
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Initial values divisible by 2^n involve in 3x+1 iteration n decreasing step, nevertheless can result peak value exceeding start-value.
|
|
LINKS
|
|
|
EXAMPLE
|
n=120=8.15,max=160>iv=120;
trajectory={120,60,30,15,46,23,70,35,106,53,160,80,40,20,10,5,16,8,4,2,1}
|
|
MATHEMATICA
|
c[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] {k=65536, ta=Table[0, {100}], u=1}; {$RecursionLimit=1000; m=0}; Do[If[Greater[Max[fpl[k*n]], k*n], Print[{k*n, n}]; ta[[u]]=k*n; u=u+1], {n, 1, 1000000}] [Code for 2^16 divisor, a(16)].
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|