[QUOTE=henryzz;443098]We are currently on 2^3. It is possible to go down with this although slowly. It doesn't take that many small factors to make it rise. We need the power of two to drop. As we have just seen, once there are no 3s or small factors that hang around long term the power of 2 will change more often.[/QUOTE]

the sequence now has 2^2.

Cmon, lets see that 2^2*p (where p is 1 mod 4)!

Shouldn't the thread title be "Sequence 4788 Episode IV: A New Hope" now?

:razz:

[QUOTE=Dubslow;443109]Cmon, lets see that 2^2*p (where p is 1 mod 4)![/QUOTE]

A line factoring as 2[sup]2k[/sup].x[sup]2l[/sup].p, p is a prime number candidate congruent to 1 (mod 4), k ≥ 1, l ≥ 1, 3 does not divide x, would be also doing fine by me too!

Why does the computation of Aliquot sequence 4788 / 314718 / 16100 oscillate up and down a lot when ever compared to computation of other Aliquot sequences?

Aliquot sequence 314718 past iteration mark 17000.
Aliquot sequence 4788 / 16100 past iteration mark 10540.
Offset iteration difference 6460.

All of the human history till year 2012 to reach out first 175 digit limit.
Four years to reach the next peak.
Few days with in year 2016 to reach 175 digits next peak.
Congratulations!

it's now caught a 3 as well as 2^2 great it's starting to climb again.... okay yeah I figured out the 3 shouldn't have anything to do with the climb as it doesn't divide 7.

Three does do with the climb, it shoots the abundance (way) above 1. And it's fairly stable too.

[COLOR="Blue"]Taking a fresh look after I just woke up this morning!
Happy autumnal equinox! Why?[/COLOR]

[QUOTE=henryzz;442223]
[COLOR="DarkOrange"]Please stop using white text I didn't notice on my first read through. Next time you do it on this subforum it will be edited to be clearer.[/COLOR][/QUOTE]

[COLOR="blue"]That is just burden on your side!
I don't think that any of the senior moderators will do that dirty work!
Posts are locked once when they are posted!
Senior moderators will not interfere with posts of other people![/COLOR]

[QUOTE=Dubslow;443201][COLOR="Green"]Three does do with the climb, it shoots the abundance (way) above 1. And it's fairly stable too.[/COLOR][/QUOTE]

[COLOR="blue"]Computation of Aliquot Sequence 4788 / 16100 / 314718 losing and gaining 3 periodically, as long as the power of 2 is a positive even number!

On the other hand,
Downdriver 2 does not ever gain a 3 unless power of 2 is mutated; Driver 2.3 does not ever lose a 3 unless power of 3 is mutated.
Stable guide 2[sup]2[/sup] does not ever gain a 7 unless power of 2 is mutated; Driver 2[sup]2[/sup].7 does not ever lose a 7 unless power of 7 is mutated.
Stable guide 2[sup]4[/sup] does not ever gain a 31 unless power of 2 is mutated; Driver 2[sup]4[/sup].31 does not ever lose a 31 unless power of 31 is mutated.
Stable guide 2[sup]6[/sup] does not ever gain a 127 unless power of 2 is mutated; Driver 2[sup]6[/sup].127 does not ever lose a 127 unless power of 127 is mutated.
Stable guide 2[sup]12[/sup] does not ever gain a 8191 unless power of 2 is mutated; Driver 2[sup]12[/sup].8191 does not ever lose a 8191 unless power of 8191 is mutated.

Ratio between computation of subsequent Aliquot / Totient sequence next iterations - Consider orbital resonance! Why?[/COLOR]

Well... technically it isn't white... maybe even overall less headache inducing than my aliquot pages :smile:

[QUOTE=Dubslow;443221]Well... technically it isn't white... maybe even overall less headache inducing than my aliquot pages :smile:[/QUOTE]

I do wonder what is going through his head sometimes. The way he pushes boundaries is like a child.

Lost the 3! Plain 2^2.

Hopefully we won't gain it again this time.