# Talk:Collatz conjecture

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Field: Number theory

## Pls look at it...

This forum is for discussion of the Wikipedia article.

The appropriate place to discuss this is the Usenet group sci.math and I've transferred it there. You can reach it via Google Groups with subject Collatz Conjecture proof?

The histogram on stopping times is very misleading.

While "valid" as stated, it is inappropriate for the distribution.

The underlying distribution has no mean (like an exponential distribution).

In fact, the actual distribution can be ( with difficulty) computed.

The essential point is the number of integers with stopping time n is a non-decreasing function of n (which is easily shown without the need to a difficult computation).

At the very least, the histogram should be complimented with the actual distribution (say though the same domain).

This would not only be illuminating, but would be a nice illustration of some subtle, yet key points about distributions (i.e. histograms are only useful with distributions with means and "small" tails). — Preceding unsigned comment added by 108.227.46.153 (talk) 15:59, 6 September 2015 (UTC)

You are certainly right in saying that the number of integers with stopping time n is a non-decreasing function of n, and the histogram clearly gives a very different impression, so I shall remove it. If you or anyone else can do put more accurate information about the distribution into the article, that will be very helpful. The editor who uses the pseudonym "JamesBWatson" (talk) 12:40, 22 March 2016 (UTC)
The number of all integers with stopping time n is equal to the number of nodes at the n-th level of the Collatz graph, which is approximately an, where 1 < a < 2, as expected from an "average" infinite tree whose nodes have one or two children.
Although this result may be interesting, it does not say anything about the expected stopping time of an integer chosen at random from a fixed interval. And that is the purpose of the removed histogram, which illustrates an important aspect of the Collatz sequence behavior. Petr Matas 19:01, 25 March 2016 (UTC)

## Longest runs

```                  2       1
3       7
6       8
7      16
9      19
18      20
25      23
27     111
54     112
73     115
97     118
129     121
171     124
231     127
313     130
327     143
649     144
703     170
871     178
1161     181
2223     182
2463     208
2919     216
3711     237
6171     261
10971     267
13255     275
17647     278
23529     281
26623     307
34239     310
35655     323
52527     339
77031     350
106239     353
142587     374
156159     382
216367     385
230631     442
410011     448
511935     469
626331     508
837799     524
1117065     527
1501353     530
1723519     556
2298025     559
3064033     562
3542887     583
3732423     596
5649499     612
6649279     664
8400511     685
11200681     688
14934241     691
15733191     704
31466382     705
36791535     744
63728127     949
127456254     950
169941673     953
226588897     956
268549803     964
537099606     965
670617279     986
1341234558     987
1412987847    1000
1674652263    1008
2610744987    1050
4578853915    1087
4890328815    1131
9780657630    1132
12212032815    1153
12235060455    1184
13371194527    1210
17828259369    1213
31694683323    1219
63389366646    1220
75128138247    1228
133561134663    1234  — Preceding unsigned comment added by Frank Klemm (talk • contribs) 23:04, 13 August 2016 (UTC)
```

## Generalized Collatz function

The cycle 0→0 is listed as 'trivial'. This is misleading since for any number other than zero, the Collatz-function cannot reach zero. There is no positive or negative natural number other than zero such that C(n)=0. It's a special case (for n=0), and should be listed or omitted as such. Kleuske (talk) 11:34, 15 September 2016 (UTC)

## History of the problem?

There is almost no history of the problem in the article, when was it first brought into serious mathematics?Naraht (talk) 13:54, 12 February 2017 (UTC)