# Collatz Patterns

I have seen documentation on the $4K+1$ pattern, but as of yet I have seen nothing on the $64K+35$ pattern or the $262144K+184471$ pattern. Is there anywhere I can read up on these?

I created the general pattern too:

$$2^{2×3^{a-1}}K + (1-\frac{2^a}{3^a}) × (2^{2×3^{a-1}}-1)$$

The 4K+1 pattern adds 2 more division steps after the first ×3+1

The 64K+35 pattern adds 6 more division steps after the second ×3+1

The 262144K+184471 pattern adds 18 more division steps after the third ×3+1

and so on..

• You are going to have to be clearer. – Thomas Andrews Jul 20 '16 at 23:15
• Should make sense now. Although I'm not sure why it didn't in the first place? The 4K+1 pattern seems to be well known. I find it hard to believe i'm the first to find these other patterns - I'm an undergrad. – Ben Crossley Jul 20 '16 at 23:21
• Sorry, but problems should best be self-contained, and you didn't say what the pattern was. If you want the most help here, it is best to be as self-contained as possible. – Thomas Andrews Jul 20 '16 at 23:44
• Cheers Thomas. I'm used to forums where people don't like to read. I will make sure of that in the future! – Ben Crossley Jul 20 '16 at 23:53
• In go.helms-net.de/math/collatz/aboutloop/collloopintro_main.htm on the page of "about numerical and graphical trees" I've examples for the 64k pattern; that all cumulated in the "bottle-brush-tree" which generalizes that stepwidths in a -hopefully- interesting view. – Gottfried Helms Jul 21 '16 at 10:16