Talk:Collatz conjecture

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 Field: Number theory

Pls look at it...[edit]

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?

Histogram is misleading[edit]

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[edit]

                  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 (talkcontribs) 23:04, 13 August 2016 (UTC) 

Generalized Collatz function[edit]

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?[edit]

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)