20210403, 15:13  #12  
"Alexander"
Nov 2008
The Alamo City
601 Posts 
Quote:


20210405, 06:34  #13  
"Garambois JeanLuc"
Oct 2011
France
2×7×41 Posts 
Quote:
I agree ! I will also be working on this soon ! 

20210411, 18:10  #14 
"Ed Hall"
Dec 2009
Adirondack Mtns
47×79 Posts 
I've added a little bit to my program. Hopefully it is of more interest than just mine. The new source code is attached.
It should compile under linux with the following command: Code:
g++ seqinfo.cpp o seqinfo The file regina_file is necessary. The program has been written such that a new regina_file can be as large as to sequence 20M. The format of any new regina_file must remain the same for the first four elements ([n,a,b,c). The (h)elp entry displays all the current functions available: Code:
Available options for the following prompts (##/h/p/p##/q/u): prompt ## displays info for sequence ## if it is within the range. h provides this text block. p lists counts of all primes that terminate a sequence within the limit of regina_file. This will take a long time to complete. Due to the large return count, the list is sent to a primescount.txt file. This file is overwritten with each run. p## searches for sequences that terminate with the prime ##. u (not available yet!) run a routine to make a file of updates. The file OE_3000000_C80.txt must be available. This will take a long time. If the file exists it will be overwritten with a new file. (y/n/c/f): prompt y performs the procedure referenced. n provides a negative response. (default if an entry is omitted) c provides a count only, without a listing. f provides a listing to screen and to results.txt. (results.txt is never removed by the program. It is only appended to. It has to be manually deleted.) Code:
Data available for sequences 2 through 14000000 Sequence endings  prime: 10644411, cycle: 205473, open: 3150115 Enter sequence (##/h/p/p##/q/u): 276 276 is open ended. List any sequences that merge with 276? (y/n/c/f): c 7696 sequences found. Enter sequence (##/h/p/p##/q/u): 13923160 13923160 is open ended. It merges with 4788. Enter sequence (##/h/p/p##/q/u): 28 28 ends in a cycle. Display cycle? (starts at entry point) (y/n/f): y 28 Display all sequences that end in this cycle? (y/n/c/f): y 28 1 sequence found. Enter sequence (##/h/p/p##/q/u): 496 496 ends in a cycle. Display cycle? (starts at entry point) (y/n/f): n Display all sequences that end in this cycle? (y/n/c/f): y 496 608 650 652 790 1294 1574 1778 2162 2582 3142 5158 368449 1492799 1535075 1767455 1842215 2256401 2974751 3157729 3837505 3873551 4018945 4170127 4605213 4669921 5076873 5251285 5616985 6977649 7349365 7463965 7505901 7589845 7601365 7675345 8109041 8697385 8837245 8924241 11035163 12856335 13157075 13384167 13631207 45 sequences found. Enter sequence (##/h/p/p##/q/u): p14604141802777 List all sequences that terminate with 14604141802777? (y/n/c/f): y 1923540 2967858 3462540 6232740 8361636 11070756 11079640 11470428 11788640 11792880 12125052 13462620 13896164 13 sequences found. Enter sequence (##/h/p/p##/q/u): 13991486 13991486 ends in a cycle. Display cycle? (starts at entry point) (y/n/f): y 19916 17716 14316 19116 31704 47616 83328 177792 295488 629072 589786 294896 358336 418904 366556 274924 275444 243760 376736 381028 285778 152990 122410 97946 48976 45946 22976 22744 Display all sequences that end in this cycle? (y/n/c/f): c 8870 sequences found. Enter sequence (##/h/p/p##/q/u): q Code:
Enter sequence (#/h/p/q/u): p Generating list of prime counts. . . 910307 unique primes found! Listing took 102791 seconds to generate. Here's a sample of primescount.txt: Code:
2: 1 3: 270105 5: 1 7: 508095 11: 203297 13: 116153 17: 57124 . . . 13245150197: 3 27422578871: 1 28112302063: 2 80727104827: 21 94164320077: 2 14604141802777: 13 Last fiddled with by EdH on 20210411 at 18:31 Reason: Added a sample fo primescount.txt. 
20210412, 05:33  #15 
"Alexander"
Nov 2008
The Alamo City
601 Posts 
As a suggestion (without looking at the code), would it be possible to treat perfect numbers as a special case? For example, instead of the above output for 28, perhaps something like:
Code:
Enter sequence (##/h/p/p##/q/u): 28 28 is a perfect number. Display all sequences that end at 28? (y/n/c/f): y 28 1 sequence found. Code:
Enter sequence (##/h/p/p##/q/u): 608 608 ends in a cycle. Display cycle? (starts at entry point) (y/n/f): y 496 Display all sequences that end in this cycle? (y/n/c/f): c 45 sequences found. Code:
Enter sequence (##/h/p/p##/q/u): 608 608 ends at perfect number 496. Display all sequences that end at 496? (y/n/c/f): c 45 sequences found. 
20210412, 12:54  #16  
"Garambois JeanLuc"
Oct 2011
France
2×7×41 Posts 
Quote:
The only thing I risk doing is adding a variable "o" in each line which will be the geometric mean of the quotients of the successive terms of the sequence. I wanted to do this really fast, but sequences that merge with other Open End sequences are problematic and need to be recalculated. I am thinking of making the change when I reach 15M, because then I will have to stop everything and modify the main program. I will probably do this in July or August ... Otherwise, I will do different tests with your program in the next few days ... 

20210412, 13:36  #17  
"Ed Hall"
Dec 2009
Adirondack Mtns
47×79 Posts 
Quote:
@garambois: Adding elements won't bother at all. I just need the front to remain the same. Are there any extra searches within regina_file that I should try adding? A side question: (From the merges/termination thread) do you have the maximum heights for sequences listed in your files? 

20210412, 15:55  #18  
"Garambois JeanLuc"
Oct 2011
France
574_{10} Posts 
Quote:
Unfortunately, I don't have the maximum heights reached by the sequences in my files ! Reminder : here is a line for a sequence of the file "regina_file" [n, a, b, c, d, e, f, g, h, i, j, k, l, m] "e" is the number of relative maxima (peaks) for the sequence that begins with the integer "n". "f" is the number of parity changes found in this sequence, that is, the number of times a perfect square or double of a perfect square is found in this sequence. I think these two data would be interesting to add to your program, because they are interesting elements which make the "identity" of a sequence. It would also be interesting to be able to classify the sequences according to their number of peaks or changes in parity. At the start of my research, I wanted to see if there was a correlation between the prime factorization of the starting numbers of the sequences and the numbers "e" and "f" (and the others of the table) or if there was a correlation between the ending prime numbers of the sequences and these "e" and "f" numbers. But I failed in this search for correlation. Your work and your program have rekindled my interest in this research ... 

20210412, 18:10  #19  
"Ed Hall"
Dec 2009
Adirondack Mtns
47×79 Posts 
Quote:
Quote:
Last fiddled with by EdH on 20210412 at 18:12 Reason: Might help to actually attach the source. 

20210412, 19:11  #20  
"Ed Hall"
Dec 2009
Adirondack Mtns
47×79 Posts 
Quote:


20210413, 14:09  #21  
"Ed Hall"
Dec 2009
Adirondack Mtns
47·79 Posts 
Quote:
I should be able to easily add a function that lists sequences based on the count but more complexities might be problematic.* What would you actually like to be able to list? * Many years ago, I used to select sequences to work on based on their graphs, expecting that the more changes, the higher probability of termination. That didn't seem to turn out as a valid indicator of a pending termination. 

20210414, 09:30  #22  
"Garambois JeanLuc"
Oct 2011
France
1076_{8} Posts 
No problem, we take the time we want. We do this for fun and if we start to feel rushed and stressed, we won't like working on these things anymore !
;) Quote:
But what if we are wrong in thinking that ? In any case, it only costs us a little time to do some tests, we could come across correlations that nobody expected ! Quote:
I have a suggestion. For example when you display all the starting numbers of the sequences that end with a prime number, personally, I tend to look at these numbers in their usual representation in base 10, but especially also in the factorized form in prime numbers : this gives us much more information about the number, which is important if we want to notice properties. Concerning e and f, I don't know if your program can show some things I would like to see. But I ask myself many questions. Let me introduce you to some ideas I've been working on recently, after Edwin started this topic. Here are some examples : 1) For each prime number, show a table that counts the number of sequences that end with that prime number that have 0 peak (this number will most likely be 0), 1 peak, 2 peaks... Example : 3 [(number of sequences that have 0 peaks and end in 3), (number of sequences that have 1 peak and end in 3), (number of sequences that have 2 peaks and end in 3), ...] 5 [(number of sequences that have 0 peaks and end with 5), (number of sequences that have 1 peak and end with 5), (number of sequences that have 2 peaks and end with 5), ...] ... The question to answer : will the distribution be the same for every prime number ? 2) A very simple way to visualize the data would also be to be able to launch a regina_file analysis by entering this in a program for example : [n%2==0, a==0, b, c, d, e==0, f, g, h, i, j, 1.7<k<2.3, l, m] Thus, for each of the 14 variables in each row of regina_file, we could specify characteristics. In the example above, the analysis would give us all the sequences that start with an even number, that are OpenEnd, that have no peak (so they are strictly increasing) and that have a slope of about 2 (so at each iteration, the size of the terms multiplies by about a factor of 2). This entry would allow us for example to find all the sequences that have the same very special graph as the sequence 19560. Thus, just for all the sequences with 0 peaks, there are several types : we could find again the drivers which are the perfect numbers by specifying a slope k rather close to 1, find the guides which ensure slopes of 2, and above all, maybe see things not yet known ... Another example : you want a bellshaped sequence. You enter : [n, a==1, b, c, d, e==1, f, g, h, i, j, 0.8<k<1.2, l, m] And you find sequences such as 2174880. Of course, the goal is to try to notice correlations between these forms of graphs and the factorization in prime factors of the starting number of the sequence (and this correlation exists at least for the sequences with 0 peaks, because of the perfect numbers drivers, of the 2perfect numbers, of the 3perfect numbers...) or according to the prime number which ends the sequences (belonging to such or such branch of the infinite graph of the aliquot sequences). I have the same questions about the number of parity changes for each sequence. But as said above, all this is a very long work started years ago. And my problem is that in python, I can't do this work anymore, because regina_file is too big. I have to work in C, and there, I'm not at ease ! 

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