## Collatz Conjecture a New Mathematical Approach.

**Authors:** Darrin Taylor

A new form of mathematics is explored where a sequence of values are acted on by a set of rules (in this case the 3n+1 rules) and each digit within the values is acted on by a subordinate set of rules which produce the same values.
But the digit rules allow patterns to be identified and calculations to be performed on mostly unknown values.
Proves that loop length must be 13x + 18y
Proves that loop is made up of segments of 8 and 11 values and names the leading digits of each value in the segments.
Shows that base 4 descent is favored on average by a factor of 5.
Shows that if the base 4 upper digits were always even sequence would always eventually descend.
Possible future work may link the leading 0s which are infinitely even can be reflected to the least significant digits over time so that over infinity the effect approaches the always even which drives descent.
Predicts loop values based on most significant base 3 digit and show quantized loop leading digits and possible pattern of increasing smallest segments.
Predict general sequence based on least significant digit base 3.
Predict general sequence based on least significant digit base 4.

**Comments:** 68 Pages. Last step of proof broke so this is merely a new mathematical framework to attack Collatz type problems

**Download:** **PDF**

### Submission history

[v1] 2019-07-09 01:25:02

[v2] 2019-08-01 03:39:38

**Unique-IP document downloads:** 35 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*