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Post Closed as "Not suitable for this site" by Daniele Tampieri, Gerald Edgar, YCor, abx, LeechLattice
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André Henriques
André Henriques
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Extreme disproportion in the dispersion of "Digital Roots" of the highest numbers reach in the Collatz Conjecture.

I calculated the Digital RootDigital Root remainder mod 9 for the highest numbers reached for each seed in Collatz Conjecture: for example, for $39$ as the seed number, the highest number reached is $304$, so the Digital Rootremainder mod 9 is $7$.
What I found is that there is a huge disporportion in the numbers obtained, most of them being $7$: in the first $100$ seed numbers, $65$ of them give $7$ as Digital Rootremainder mod 9.
I checked the pattern even for random numbers: they mostly led to $7$ (for example $111$, $222$, $333$, $444$, $555$, $666$, $777$, $888$, $999$ all lead to $7$).
For a normal set of natural numbers the Digital Rootremainder mod 9 would be proportionally distributed between $1$ and $9$, so I cannot find any reason for this strange behavior.

My questions.
Can anyone explain this phenomenon? Or is there any paper/monograph about it? Has anyone seen this phenomenon before?

Extreme disproportion in the dispersion of "Digital Roots" of the highest numbers reach in the Collatz Conjecture.

I calculated the Digital Root for the highest numbers reached for each seed in Collatz Conjecture: for example, for $39$ as the seed number, the highest number reached is $304$, so the Digital Root is $7$.
What I found is that there is a huge disporportion in the numbers obtained, most of them being $7$: in the first $100$ seed numbers, $65$ of them give $7$ as Digital Root.
I checked the pattern even for random numbers: they mostly led to $7$ (for example $111$, $222$, $333$, $444$, $555$, $666$, $777$, $888$, $999$ all lead to $7$).
For a normal set of natural numbers the Digital Root would be proportionally distributed between $1$ and $9$, so I cannot find any reason for this strange behavior.

My questions.
Can anyone explain this phenomenon? Or is there any paper/monograph about it? Has anyone seen this phenomenon before?

Extreme disproportion in the dispersion of "Digital Roots" of the highest numbers reach in the Collatz Conjecture.

I calculated the Digital Root remainder mod 9 for the highest numbers reached for each seed in Collatz Conjecture: for example, for $39$ as the seed number, the highest number reached is $304$, so the remainder mod 9 is $7$.
What I found is that there is a huge disporportion in the numbers obtained, most of them being $7$: in the first $100$ seed numbers, $65$ of them give $7$ as remainder mod 9.
I checked the pattern even for random numbers: they mostly led to $7$ (for example $111$, $222$, $333$, $444$, $555$, $666$, $777$, $888$, $999$ all lead to $7$).
For a normal set of natural numbers the remainder mod 9 would be proportionally distributed between $1$ and $9$, so I cannot find any reason for this strange behavior.

My questions.
Can anyone explain this phenomenon? Or is there any paper/monograph about it? Has anyone seen this phenomenon before?

Math Jaxed, minor grammar and typo fixes
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Daniele Tampieri
Daniele Tampieri
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Extreme disproportion in the dispersion of "Digital Roots" of the highest numbers reach in the Collatz ConjunctureExtreme disproportion in the dispersion of "Digital Roots" of the highest numbers reach in the Collatz Conjecture.

I calculated the Digital Root for the highest numbers reached for each seed in Collatz Conjuncture.Conjecture: for example, for 39$39$ as the seed number, the highest number reached is 304$304$, so the Digital Root is 7$7$. 
whatWhat I found is that there is a huge disporportion in the numbers obtained, most of them being 7. In$7$: in the first 100$100$ seed numbers, 65$65$ of them give 7$7$ as Digital Root. 
evenI checked the pattern even for random numbers I checked,: they mostly led to 7$7$ (for example 111$111$, 222$222$, 333$333$, 444$444$, 555$555$, 666$666$, 777$777$, 888$888$, 999$999$ all lead to 7$7$).
since forFor a normal set of natural numbers, the Digital Root would be porportionallyproportionally distributed between 1$1$ and 9$9$, so I can'tcannot find any reason for this strange behavior.

My questions.
canCan anyone explain this phenomenon? orOr is there any textpaper/monograph about thisit? hasHas anyone checkedseen this phenomenon before?

Extreme disproportion in the dispersion of "Digital Roots" of the highest numbers reach in the Collatz Conjuncture

I calculated the Digital Root for the highest numbers reached for each seed in Collatz Conjuncture. for example for 39 as the seed number, the highest number reached is 304, so the Digital Root is 7. what I found is that there is a huge disporportion in the numbers, most of them being 7. In the first 100 seed numbers, 65 of them give 7. even for random numbers I checked, they mostly led to 7 (for example 111, 222, 333, 444, 555, 666, 777, 888, 999 all lead to 7) since for a normal set of natural numbers, the Digital Root would be porportionally distributed between 1 and 9, I can't find any reason for this. can anyone explain this? or is there any text about this? has anyone checked this before?

Extreme disproportion in the dispersion of "Digital Roots" of the highest numbers reach in the Collatz Conjecture.

I calculated the Digital Root for the highest numbers reached for each seed in Collatz Conjecture: for example, for $39$ as the seed number, the highest number reached is $304$, so the Digital Root is $7$. 
What I found is that there is a huge disporportion in the numbers obtained, most of them being $7$: in the first $100$ seed numbers, $65$ of them give $7$ as Digital Root. 
I checked the pattern even for random numbers: they mostly led to $7$ (for example $111$, $222$, $333$, $444$, $555$, $666$, $777$, $888$, $999$ all lead to $7$).
For a normal set of natural numbers the Digital Root would be proportionally distributed between $1$ and $9$, so I cannot find any reason for this strange behavior.

My questions.
Can anyone explain this phenomenon? Or is there any paper/monograph about it? Has anyone seen this phenomenon before?

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Sir.Otonin
Sir.Otonin
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Can you explain this weird pattern in Collatz conjecture?

Extreme disproportion in the dispersion of "Digital Roots" of the highest numbers reach in the Collatz Conjuncture

I calculated the Digital Root for the highest numbers reached for each seed in Collatz Conjuncture. for example for 39 as the seed number, the highest number reached is 304, so the Digital Root is 7. what I found is that there is a huge disporportion in the numbers, most of them being 7. In the first 100 seed numbers, 65 of them give 7. even for random numbers I checked, they mostly led to 7 (for example 111, 222, 333, 444, 555, 666, 777, 888, 999 all lead to 7) since for a normal set of natural numbers, the Digital Root would be porportionally distributed between 1 and 9, I can't find any reason for this. can anyone explain this? or is there any text about this? has anyone checked this before?