mersenneforum.org Aliquot genealogy project
 Register FAQ Search Today's Posts Mark Forums Read

 2012-01-04, 08:14 #56 wolfcrey     Jul 2009 Aachen, Germany 1010012 Posts In 1988 I wrote a small programme for pocket calculator for a backward-calculation of an aliquot sequence. It was transformed in UBASIC and runs well. I published some ideas from Jack Alanan in my book "Primzahlfamilien", too. I zipped the total packet: http://www.aliquot.de/archiv/retour.zip The progamme will run in a DOS-Window. You can study the code of retour.ub and ingold.ub for transforming it on modern PCs. All the best for 2012 and many following years Wolfgang
 2012-01-04, 09:43 #57 wolfcrey     Jul 2009 Aachen, Germany 41 Posts 0 : 104 1 : 104 ist der Inhalt von 10609 2 : 104 ist der Inhalt von 202 Der Grad der ZAHL 104 ist : g(104) >= 2 Mit mehrfaktorigen Zerlegungen ist der Grad der ZAHL 104 jetzt: g(104) >= 2 0 : 102 1 : 102 ist der Inhalt von 10201 Der Grad der ZAHL 102 ist : g(102) >= 1 Mit mehrfaktorigen Zerlegungen ist der Grad der ZAHL 102 jetzt: g(102) >= 1 0 : 96 0 : 96 ist vermutlich unberührt Die ZAHL 96 ist vermutlich unberührt, ihr Grad ist 0 Mit mehrfaktorigen Zerlegungen ist der Grad der ZAHL 96 jetzt: g(96) >= 0
2012-01-05, 03:10   #58
kar_bon

Mar 2006
Germany

54358 Posts
Changed version

I've used a different algorithm to calculate and print the sequences.

- no double edges or missing (for example n=104 ending in 41p)
- all perfect/amicable displayed correct (like 496 or 1182/1210)
- "Open Sequences" printed when greater as a given maximum (mostly on righthand side)
- 'lonely' values like '5' not printed
- the code is much smaller (~ 90 with comments against ~200 lines)

Inlcuded is the graph-file for dotty for the range up to n=2000 and the lua-source.

I've tested also n=10000 but dotty needs some time to display and will not show the whole range of sequences (dotty-dispaly to small for all).

I've not yet displayed special shapes like to original version.

Please test/play with and tell errors.
Attached Files
 lua_ali.zip (9.6 KB, 61 views)

Last fiddled with by kar_bon on 2012-01-05 at 03:21

 2012-01-05, 06:12 #59 firejuggler     Apr 2010 Over the rainbow 45538 Posts Writing sequence with only one "->" really helped. It was stupid to think about writing the entire sequence in one go. to get the odd in plaintext and the circle shape for "perfect" change the second loop to Code:  for i=3, range do -- for the given range try to make the sequences while sigma[i] ~= nil and nsigma[i] ~= nil do -- avoid to display lonely values, which were never reached if sigma[i] > 100000 then -- maximum reached -> display as "Open Sequence" io.write(i.."[label=\"OpenSeq\",shape=plaintext];\n") nsigma[i] = nil break end if sigma[i] == 1 then -- values reached is prime -> mark as "Prime" io.write(i.."[label=\""..i.."p\",shape=plaintext];\n") else io.write(i.."->"..sigma[i].."\n") -- else normal value if i==sigma[i] then io.write(i.."[shape=circle];\n") end end nsigma[i] = nil -- mark edge as already printed (no doubles) i = sigma[i] if i%2==1 then io.write(i.."[shape=plaintext];\n") end end end now the hard part, to detect "merge". boxes should happen what at least 2 arrow point to a number and triangle should (that will probably hard and need a third loop) happen when the lowest even number leading to that merge Code: 102->114 114->126 126->186 174->186 186[shape=box]; 102[shape=triangle];
2012-01-06, 20:19   #60
kar_bon

Mar 2006
Germany

5·569 Posts

Quote:
 Originally Posted by firejuggler now the hard part, to detect "merge". boxes should happen what at least 2 arrow point to a number and triangle should (that will probably hard and need a third loop) happen when the lowest even number leading to that merge Code: 102->114 114->126 126->186 174->186 186[shape=box]; 102[shape=triangle];
The first hard part is implemented:
- detect merges and ouput those nodes as box
- also perfect numbers and amicable pairs are solved: shown as circle

Included the updated source and the graph-file up to n=2000.

The harder part with lowest value for a merge is still missing yet.
Attached Files
 lua_ali.zip (11.1 KB, 57 views)

2012-01-15, 04:46   #61
kar_bon

Mar 2006
Germany

5·569 Posts

I've done a first version of a LUA-program to build a graph backwards from a given sequence with all merges lesser than 1000000.

First I've build a file with all sigma-values for n<=1000000 (4 bytes for each sequence-value, so maximum is 4294967295; highest sigma is 3392928 for seq=997920; the file can be extended easily), so the sigmas only have to be calculated once.

For a given seq this file is loaded and the tree is build recursively.

So far the main sequence is filled with lightblue and the index of the value is given.
No shapes yet considered (for example: box for odd values).

A GIF-image for the 276-tree can be found here (730 kB) (got problems to view in IE, but FF worked).

The graph-source file for Graphviz is attached.

Please check first before code is given.
Attached Files
 276.txt (10.2 KB, 91 views)

 2012-01-15, 15:33 #62 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 2×7×239 Posts Wow! This is fantastic. I had no idea so many numbers merged into others... So, if/when 276 terminates, all these others will, too. This image is a great eye opener for me. Thanks for the effort you put in.
 2012-01-15, 16:08 #63 chris2be8     Sep 2009 22×11×43 Posts Is anyone working on 276? The c162 is doable given time. Chris K
2012-01-15, 16:33   #64
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2·1,061 Posts

Quote:
 Originally Posted by chris2be8 Is anyone working on 276? The c162 is doable given time. Chris K
Paul Zimmermann has been handling the Lehmer Five. You could email him and see what his plans are.

However, until the 2 * 3 driver is lost, it is essentially hopeless. (966 was doing pretty badly, too, but I see it has escaped 2^3 * 3; now it just needs to lose the '3'.)

 2012-01-15, 16:42 #65 kar_bon     Mar 2006 Germany B1D16 Posts Here's the graph for seq 4788 (this time a PNG; 14523 x 3087 pixel; 1,5 MB). There're 1022 seqs (incl. 4788) < 1000000 in this family. The 'real' 4788-tree is rightmost only a little bonsai, but with a big branch of about 1000 seqs! Last fiddled with by kar_bon on 2012-01-15 at 16:43 Reason: 1M
2012-01-15, 16:55   #66
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by schickel Paul Zimmermann has been handling the Lehmer Five. You could email him and see what his plans are. However, until the 2 * 3 driver is lost, it is essentially hopeless. (966 was doing pretty badly, too, but I see it has escaped 2^3 * 3; now it just needs to lose the '3'.)
oh thanks that's the driver I have supposedly right now at last check lmao .

 Similar Threads Thread Thread Starter Forum Replies Last Post firejuggler Aliquot Sequences 26 2012-01-19 08:15 schickel Aliquot Sequences 307 2011-10-28 01:29 JohnFullspeed Aliquot Sequences 18 2011-08-20 21:11 schickel Aliquot Sequences 29 2011-08-12 17:45 Andi47 Aliquot Sequences 3 2009-03-08 10:18

All times are UTC. The time now is 13:05.

Thu Sep 24 13:05:30 UTC 2020 up 14 days, 10:16, 2 users, load averages: 1.61, 1.88, 1.80