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2021-04-23, 06:25   #45
Happy5214

"Alexander"
Nov 2008
The Alamo City

2·3·5·23 Posts

Quote:
 Originally Posted by garambois If I understand your question correctly, in this database, at no time do I distinguish between guides or drivers or "downdrivers". On the other hand, in the new database, for each sequence, we will have the following line : n, a, b, c, d, e, f, g, h, i, j, k, l, m, o, t And as explained on this page, here is the meaning of the variables g, h, i, j : g : record number of strictly increasing even consecutive terms in the starting sequence n. h : record number of strictly decreasing even consecutive terms in the starting sequence n. i : record number of strictly decreasing odd consecutive terms in the starting sequence n. j : record number of strictly increasing odd consecutive terms in the starting sequence n. The variable h therefore does indeed count the number of terms of the largest decreasing "extract" of consecutive even terms of the sequence.
Not technically the same thing, as downdriver runs can sometimes have brief blips where they go up (think of 2*5*7). I was thinking more of the number of distinct runs, not the length of runs.

Quote:
 Originally Posted by garambois The variables o and t will be the terms added compared to the old database : o : Geometric mean of the terms of the sequence. t : bigger term in the sequence.
T? Shouldn't that be P?

Quote:
 Originally Posted by garambois I hope I answered your question and do not hesitate if not ... And above all, don't hesitate to give me your ideas if you think I still need to add an additional variable.
Two new related ideas: the average of the relative maxima and the average of the relative minima.

Quote:
 Originally Posted by garambois As for the name "regina", there are two reasons : 1) In a way, this database is the "queen" of databases, in a way the "fundamental database" on aliquot sequences. 2) For the little anecdote, my wife's first name is "Régine" and I developed the idea of this program in particular circumstances. Régine and I were going on vacation, in the car, crossing Switzerland, without having any computer, just a sheet of paper and a pencil. Régine, who was driving next to me, was looking at me with funny eyes, wondering what I was doing, instead of looking at the breathtakingly beautiful landscapes with the snow-capped Alps.
Cute story. It was Earth Day Thursday, and I'm bummed at how the glaciers are all melting. Enjoy them while you can.

2021-04-23, 08:14   #46
garambois

"Garambois Jean-Luc"
Oct 2011
France

12008 Posts

Quote:
 Originally Posted by Happy5214 Not technically the same thing, as downdriver runs can sometimes have brief blips where they go up (think of 2*5*7). I was thinking more of the number of distinct runs, not the length of runs.
Sorry, but isn't that the same number as the number of relative maximums given by variable "e"?

Quote:
 Originally Posted by Happy5214 T? Shouldn't that be P?
I don't think the variable names matter, it won't change anything. This name will not appear in the database, just where I will explain the meaning of each number in the row. Is not it ? But if that suits you, we can call it p.

Quote:
 Originally Posted by Happy5214 Two new related ideas: the average of the relative maxima and the average of the relative minima.
Are you talking about arithmetic or geometric means ?
And you are talking about the averages of the terms of the maxima and minima or the averages of the number of digits of these terms ?

I haven't started running the program yet, because I still changed a few lines of code and ran speed tests with different settings.
But I will wait for your response to this message, to find out which averages of the maxima and minima would be useful to you.
Because this will add two variables and I will still have to modify the program.
If I add these two variables after the other 15, the order of the variables will also be quite weird : maybe I should change the order of the variables so that all the means are "close".
Do you have an opinion on the order of the variables ?

2021-04-23, 23:14   #47
Happy5214

"Alexander"
Nov 2008
The Alamo City

12628 Posts

Quote:
 Originally Posted by garambois Sorry, but isn't that the same number as the number of relative maximums given by variable "e"?
A downdriver can mutate to 2^2 or another 2^n (without the associated small factor that creates a driver/guide) and still be going down, but that's not necessarily a "decreasing regime" by my definition.

Quote:
 Originally Posted by garambois Are you talking about arithmetic or geometric means ? And you are talking about the averages of the terms of the maxima and minima or the averages of the number of digits of these terms ?
Sorry, I should have been clearer. Arithmetic mean of the digit counts is fine. Geometric means wouldn't make sense since we're not really explicitly working with growth rates, and using the whole number rather than the digit count is overkill.

Quote:
 Originally Posted by garambois I haven't started running the program yet, because I still changed a few lines of code and ran speed tests with different settings. But I will wait for your response to this message, to find out which averages of the maxima and minima would be useful to you. Because this will add two variables and I will still have to modify the program. If I add these two variables after the other 15, the order of the variables will also be quite weird : maybe I should change the order of the variables so that all the means are "close". Do you have an opinion on the order of the variables ?
Yeah, I would move L and M to after J and sort P before E, unless you end up doing the downdriver stat that I proposed, which I would put between J and L, and sort the means at the end. It would be [n, a, b, c, d, p, e, f, g, h, i, j, q?, l, m, k, o].

Last fiddled with by Happy5214 on 2021-04-23 at 23:18

2021-04-24, 07:51   #48
garambois

"Garambois Jean-Luc"
Oct 2011
France

27·5 Posts

First of all, thank you very much Happy for your interest in this work.
I think the database will be even richer now !

1) I will add the two arithmetic means you ask for and I will change the order of the variables, it will be much clearer this way.

2) I will add another variable : the number of minimums encountered in a sequence. This is not necessarily the same as the number of maximums, for example in the case of a sequence with a V-shaped graph.

Quote:
 Originally Posted by Happy5214 A downdriver can mutate to 2^2 or another 2^n (without the associated small factor that creates a driver/guide) and still be going down, but that's not necessarily a "decreasing regime" by my definition.
3) Now I have the problem with the variable q.
I still do not understand what you are suggesting.
Let me make up a digital example below with a fictitious sequence (deficient terms in red, abundant terms in black, c is a cofactor without the 3) :

index. term

0. 2*c
1. 2^2*c
2. 2^2*c
3. 2^3*c
4. 2^3*c
5. 2^3*c
6. 2*3*c
7. 2*3*c
8. 2*c
9. 2*c
10. 2*c
11. 2*c
12. 2^2*c
13. 2^2*c
14. 2^2*c
15. 2^2*c
16. 2^2*c
17. 2^3*c
18. 2^3*c
19. 2^3*c
20. 2^3*c
21. 2^3*c
22. 2^3*c

Please, what is the number q in this example, and why ?

2021-04-25, 06:36   #49
Happy5214

"Alexander"
Nov 2008
The Alamo City

2·3·5·23 Posts

Quote:
 Originally Posted by garambois 3) Now I have the problem with the variable q. I still do not understand what you are suggesting. Let me make up a digital example below with a fictitious sequence (deficient terms in red, abundant terms in black, c is a cofactor without the 3) : index. term 0. 2*c 1. 2^2*c 2. 2^2*c 3. 2^3*c 4. 2^3*c 5. 2^3*c 6. 2*3*c 7. 2*3*c 8. 2*c 9. 2*c 10. 2*c 11. 2*c 12. 2^2*c 13. 2^2*c 14. 2^2*c 15. 2^2*c 16. 2^2*c 17. 2^3*c 18. 2^3*c 19. 2^3*c 20. 2^3*c 21. 2^3*c 22. 2^3*c Please, what is the number q in this example, and why ?
The answer is 2, for the downdriver runs 0-0 and 8-11. I defined "decreasing regime" above as downdrivers and odd terms (i.e. no 2 at all), so 2^2 and 2^3 don't count, even if they're deficient. They can start increasing much more easily than a downdriver without mutating first, especially 2^2, while a downdriver term can only really be abundant with 2*5*7 or some other combination of 3 or more small factors along with the 2 (not even 2*5*11 is abundant on its own).

 2021-04-25, 17:41 #50 garambois     "Garambois Jean-Luc" Oct 2011 France 27×5 Posts Thank you all very much for your advice and ideas. The new "regina" program is finally running ... and it calculates 19 variables for each sequence. I will make final checks during this week and I will keep you posted ...
2021-05-02, 22:02   #51
EdH

"Ed Hall"
Dec 2009

3,823 Posts

Quote:
 Originally Posted by garambois Thank you all very much for your advice and ideas. The new "regina" program is finally running ... and it calculates 19 variables for each sequence. I will make final checks during this week and I will keep you posted ...
Jean-Luc, Could you post a sample of your new file, with the new key for the changed elements? I'm hoping to work some more on getting the latest version to work with both formats. I am also trying to add some "features" but some of them are still giving me a bit of a challenge. -Ed

2021-05-04, 16:59   #52
garambois

"Garambois Jean-Luc"
Oct 2011
France

27·5 Posts

Quote:
 Originally Posted by EdH Jean-Luc, Could you post a sample of your new file, with the new key for the changed elements? I'm hoping to work some more on getting the latest version to work with both formats. I am also trying to add some "features" but some of them are still giving me a bit of a challenge. -Ed
In the attachment you can find the new file "regina" up to 1e5.
To explain the meaning of all the variables in this file, I think it is much easier to take the letters of the alphabet in order and explain the meaning of each variable.
Each line of the file represents a sequence and is written like this :

[A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T]

A : starting integer of the aliquot sequence.
B : relative integer which is 1 if the aliquot sequence from start A ends up at 1, which is 0 if the sequence is open-end, which is negative if the sequence falls on a cycle of length |B|, with |B| being the absolute value of B.
C : number of iterations at the end of the computation of the sequence. We stop the calculation if we end up with 1, if we find a cycle or if the terms are greater than 10^50 and we consider it as an open-end sequence (or if the sequence meets a term of 25 digits of an open-end sequence already calculated previously, to decrease the calculation time).
D : if B is 1, D is the prime number on which the starting sequence A fell. If B is 0, D is the smallest starting integer of the open-end sequence merged by the starting sequence A. If B is negative, D is the integer belonging to the cycle by which the starting sequence A entered this cycle.
E : if B is 1, E tells for how many other sequences one has already fallen on the prime number D, including the starting sequence A. If B is 0, E tells for how many other sequences one has already fallen on the open-end beginning with D, including the starting sequence A. If B is negative, E tells for how many other sequences one has already fallen on the same cycle, including the starting sequence A.
F : number of digits of the largest term of the starting sequence A.
G : number of relative minimums of the starting sequence A.
H : number of relative maximums encountered in the starting sequence A.
I : number of parity changes encountered in the starting sequence A.
J : record number of consecutive even abundant terms in the starting sequence A.
K : record number of consecutive even deficient terms in the starting sequence A.
L : record number of consecutive odd deficient terms in the starting sequence A.
M : record number of consecutive odd abundant terms in the starting sequence A.
N : number of downdriver extracts in the sequence : terms of the form 2^1 * cofactor with 3 which does not divide cofactor.
O : smallest quotient of two consecutive terms su+1(A)/su(A) found in the whole starting sequence A, except the last quotient if B=1 and A not prime (if A is prime, the only quotient is the last quotient and it has no sense, because the last but one term of the aliquot sequence is prime and so the last quotient can be very small if this prime number is large).
P : largest quotient of two consecutive terms su+1(A)/su(A) found in the whole starting sequence A.
Q : arithmetic mean of su+1(A)/su(A), that is to say arithmetic mean of all the quotients of two consecutive terms of the starting sequence A, except for the last quotient if B=1 (this last quotient is the unique one if A is prime and in this last case, we count it anyway). We make the sum of all su+1(A)/su(A), 0<=u<=C, and we divide it by the number C; or by C-1 if B=1 and if A is not prime.
R : geometric mean of su+1(A)/su(A), i.e. geometric mean of all the quotients of two consecutive terms of the starting sequence A, except for the last quotient if B=1 (this last quotient is the only one if A is prime and in this last case, it is counted anyway). We make the product of all su+1(A)/su(A) with 0<=u<=C, that comes back to consider finally only the quotient of the last term of the sequence by the first term, and we raise this exponent to the power 1/C ; or by C-1 if B=1 and if A is not prime. Be careful with the entry in the cycles : here, we only count all the members of the cycle once. But if we want another geometric mean, we can find it with the other parameters of the line. For example, we can want the geometric mean of the sequence without the cycle, or by counting the number of entries in the cycle twice...
S : arithmetic mean of the number of digits of all the minimums of the sequence.
T : arithmetic mean of the number of digits of all the maximums of the sequence.

Here are some lines from the regina file as an example :

2,1,1,2,1,1,0,0,1,0,0,0,0,1,0.5000000000,0.5000000000,0.5000000000,0.5000000000,0,0
3,1,1,3,1,1,0,0,0,0,0,1,0,0,0.3333333333,0.3333333333,0.3333333333,0.3333333333,0,0
4,1,2,3,2,1,0,0,1,0,0,1,0,0,0.7500000000,0.7500000000,0.7500000000,0.7500000000,0,0
5,1,1,5,1,1,0,0,0,0,0,1,0,0,0.2000000000,0.2000000000,0.2000000000,0.2000000000,0,0
6,-1,1,6,1,1,0,0,0,0,0,0,0,0,1.000000000,1.000000000,1.000000000,1.000000000,0,0
7,1,1,7,1,1,0,0,0,0,0,1,0,0,0.1428571429,0.1428571429,0.1428571429,0.1428571429,0,0
8,1,2,7,2,1,0,0,1,0,0,1,0,0,0.8750000000,0.8750000000,0.8750000000,0.8750000000,0,0
9,1,3,3,3,1,0,0,2,0,0,1,0,0,0.4444444444,0.7500000000,0.5972222222,0.5773502692,0,0
10,1,3,7,3,2,0,0,1,0,1,1,0,1,0.8000000000,0.8750000000,0.8375000000,0.8366600265,0,0
11,1,1,11,1,2,0,0,0,0,0,1,0,0,0.09090909091,0.09090909091,0.09090909091,0.09090909091,0,0
12,1,6,3,4,2,0,1,3,1,0,1,0,0,0.4444444444,1.333333333,0.8130555555,0.7578582833,0,2.000000000
13,1,1,13,1,2,0,0,0,0,0,1,0,0,0.07692307692,0.07692307692,0.07692307692,0.07692307692,0,0
14,1,4,7,4,2,0,0,1,0,2,1,0,1,0.7142857143,0.8750000000,0.7964285714,0.7937005260,0,0
...
...
138,1,177,59,2,12,14,15,1,31,37,2,0,9,0.2226415094,2.472557387,1.097090035,0.9951837026,5.714285714,6.533333333
...
...
276,0,491,276,1,51,30,30,0,164,55,0,0,2,0.5000000000,2.918415621,1.365056702,1.250148383,26.43333333,27.03333333
277,1,1,277,1,3,0,0,0,0,0,1,0,0,0.003610108303,0.003610108303,0.003610108303,0.003610108303,0,0
278,1,6,43,42,3,1,1,1,1,3,1,0,2,0.5107913669,1.250000000,0.7364917336,0.6884695423,2.000000000,2.000000000
279,1,2,137,2,3,0,0,0,0,0,2,0,0,0.4910394265,0.4910394265,0.4910394265,0.4910394265,0,0
280,1,15,41,31,3,2,3,1,3,6,2,0,2,0.5066079295,1.571428571,0.9314937741,0.8717698494,2.500000000,2.666666667
281,1,1,281,1,3,0,0,0,0,0,1,0,0,0.003558718861,0.003558718861,0.003558718861,0.003558718861,0,0
282,1,16,163,2,5,0,1,1,11,0,4,0,0,0.1080225678,1.971428571,1.188064593,0.9641158730,0,5.000000000
283,1,1,283,1,3,0,0,0,0,0,1,0,0,0.003533568905,0.003533568905,0.003533568905,0.003533568905,0,0
284,-2,2,284,2,3,1,0,0,1,1,0,0,0,0.7746478873,1.290909091,1.032778489,1.000000000,3.000000000,0
...
...
306,0,144,276,2,26,1,1,0,136,2,0,0,1,0.8047493404,2.872578052,1.512782551,1.437485463,4.000000000,4.000000000

For information, after almost 10 days of calculation, I am at 2.5 M.
Don't hesitate to let me know if something is not clear to you, I had a hard time explaining all this in English !
Don't hesitate either if you find an anomaly in the file !
Attached Files
 regina_file_1e5.tar.gz (3.13 MB, 25 views)

 2021-05-04, 23:59 #53 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 3,823 Posts Thanks! I'll let you know how it turns out. It may be a while, but let's see where it goes. . .
2021-05-11, 15:15   #54
EdH

"Ed Hall"
Dec 2009

3,823 Posts
Version 2 of seqinfo

Here is the new version of the tool, which I'm calling "seqinfo2." Of course, it can be named anything one wishes when it is compiled, but I will refer to it as seqinfo2.

This file was written to read the entire NEW version of regina_file (up to 20M). It will not work with the older version, which has a different order and number of elements per line. The default filename is coded as regina_file, but an alternate name can be provided on the command line, e.g. "regina_file_1e5" for the 2-100000 set.

The biggest addition to this version is the ability to do "Advanced Searches" of the data. All of the regina-file is read into memory, so be sure your machine has a fair amount of RAM.

Since many of the new fields contain precision values, (almost) all entries for the Advanced Search function are set up to accept up to two values separated by a space. In the case of the first entry, which filters the sequence values, the entry is made in the form of a and b, where a (mod b) will be evaluated. To choose 3 (mod 7), enter "3 7" (without quotes) and the values of 3, 10, 17, ... will be evaluated. A single value equals 0 (mod <value>) and leaving the entry blank equals 0 (mod 1), evaluating all sequences in the full list.

The next entry is for the range of sequences and is inclusive. If a single value is entered, it is the range. If this entry is left blank, the entire set is evaluated.

The third entry is the only one that expects a single letter to choose whether to limit the search to primes, open-endeds or cycles. A blank entry is treated as "all."

All the rest of the entries are of the "min max" format and a single entry is treated as both values. A blank entry is treated as the range being 0 to 10000, which should mean all values.*

* Note: If any values other than element B can be <0, let me know, so I can change the program to include them.

The source should compile under linux with "g++ seqinfo2.cpp -o seqinfo2" on the command line and should run with "./seqinfo2" (or "./seqinfo2 <alternate filename>") in a terminal. If any messages are returned when compiling, let me know of them.
Attached Files
 seqinfo2.cpp (36.2 KB, 17 views)

2021-05-13, 09:08   #55
garambois

"Garambois Jean-Luc"
Oct 2011
France

64010 Posts

Thanks Edwin for all your hard work !
I have some questions, remarks, answers, information...

1) Would it be possible to show us an example of an entry to achieve an "Advanced Search" ?

2) After less than 3 weeks of computation, the new program came to more than 4,000,000. So I think it should reach 20 M sometime this summer. But then, the RAM needed to run the program should become too large for almost all computers, unless I am wrong ! For sequences up to 20 M, the file will be over 2 GB. And in python, in my experience, it is impossible to process such a file by storing it in RAM : it takes much more memory than the file size. But maybe it's different in C, I hope so !

3) Just for information, I am thinking of letting the program run for several months and this new program could process all the sequences up to 50 M, or even more... if my old computer does not break down.

4)
Quote:
 Originally Posted by EdH * Note: If any values other than element B can be <0, let me know, so I can change the program to include them.
There can be no other negative value than B in the table, that is for sure.

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