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-   -   Aliquot sequences that start on the integer powers n^i (https://www.mersenneforum.org/showthread.php?t=23612)

EdH 2022-02-23 12:58

[QUOTE=garambois;600567]. . .
In a short time, we will have 7 more bases on our page.
We will then only have 8 bases left to initialize to have all the bases <100.
. . .
[/QUOTE]Would it be more valuable to the project for me to initialize a new base or continue with the larger exponents for base 98?

garambois 2022-02-23 13:58

[QUOTE=EdH;600571]Would it be more valuable to the project for me to initialize a new base or continue with the larger exponents for base 98?[/QUOTE]

I really think that those with significant computing power, if they want to, can try to green the trivial sequences for the large exponents of the bases.
So, I think it would be excellent if you stayed on the large exponents of base 98 first.
That doesn't prevent you from initializing new bases as well, but for you it will be much faster than for me.
It is always a pleasure to initialize new bases.

It would also be extremely interesting to calculate and finish the trivial sequences of the large exponents of the small bases, like bases 3, 5, 6, 7 and 10. But these bases are reserved for yoyo and I don't know exactly for which exponents yoyo is blocked !
In a few months, I should also have a much more powerful machine.
And it is extremely likely that I will extend these small bases by adding exponents to them.
For base 2, I will certainly extend to exponent 600.
For base 3, I will certainly extend to exponent 400.
For base 5, I will certainly extend to exponent 280 or even better 300...
This would allow us to discover a whole family of curves with very strong decay according to the idea exposed in [URL="https://www.mersenneforum.org/showpost.php?p=592117&postcount=1360"]this post[/URL] : curves which would be constituted by points materialized by exponents all the larger as the base is small (for a given prime number).

Moreover, in a short time, when we will have all the bases up to 100, for the continuation, I will have to look at which type of bases it would be necessary to privilege : the prime numbers (I make tests according to this idea since a few weeks), the doubles of squares, the factorials...
Unfortunately, this whole project is almost only based on intuition.
But what else do we have than our intuition to attack the problems concerning the aliquot sequences ?

RichD 2022-02-24 21:33

Base 92 can be added at the next update.

kruoli 2022-02-25 20:45

Is it wished for to initialize base 127? If so, I would like to do this after base 94. The latter is nearing completion up to 120 digits from exponents 1 to 100.

garambois 2022-02-26 14:26

[QUOTE=RichD;600690]Base 92 can be added at the next update.[/QUOTE]
A lot of thanks !
The base 92 is now added on the page : the sequence of exponent 21 ends with a cycle !


Base 660 corrected, an error was present for exponent 6.


[QUOTE=kruoli;600744]Is it wished for to initialize base 127? If so, I would like to do this after base 94. The latter is nearing completion up to 120 digits from exponents 1 to 100.[/QUOTE]
Of course, it's great if you get into the calculations for base 127 !
For base 94, if you calculate all sequences up to 100 digits for all exponents up to 100, then you are doing much more than just initializing that base !
A lot of thanks !

RichD 2022-02-27 13:33

Base 93 can be added at the next update.


Taking bases 90 & 91 to initialize.

RichD 2022-03-02 13:22

Base 91 can be added at the next update.

garambois 2022-03-02 18:21

OK, many thanks RichD.
Many thanks to all.

[B]Added bases : 91 and 93.[/B]
[B]Some bases on which I work updated.[/B]

Don't hesitate to let me know which databases you work on regularly, so I can include them in the next partial updates.

richs 2022-03-02 19:42

I have been working on 385^4.

garambois 2022-03-02 20:00

Thank you for letting me know.
You have to refer to the blue page.
I saw on the blue page that you have reserved the sequence with which 385^4 merges, that is : 903872.

RichD 2022-03-03 02:57

Base 90 can be added at the next update.


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