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Old 2012-01-04, 08:14   #56
wolfcrey
 
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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
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Old 2012-01-04, 09:43   #57
wolfcrey
 
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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
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Old 2012-01-05, 03:10   #58
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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
File Type: zip lua_ali.zip (9.6 KB, 61 views)

Last fiddled with by kar_bon on 2012-01-05 at 03:21
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Old 2012-01-05, 06:12   #59
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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];
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Old 2012-01-06, 20:19   #60
kar_bon
 
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Quote:
Originally Posted by firejuggler View Post
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
File Type: zip lua_ali.zip (11.1 KB, 57 views)
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Old 2012-01-15, 04:46   #61
kar_bon
 
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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
File Type: txt 276.txt (10.2 KB, 91 views)
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Old 2012-01-15, 15:33   #62
EdH
 
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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.
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Old 2012-01-15, 16:08   #63
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Is anyone working on 276? The c162 is doable given time.

Chris K
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Old 2012-01-15, 16:33   #64
schickel
 
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Quote:
Originally Posted by chris2be8 View Post
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'.)
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Old 2012-01-15, 16:42   #65
kar_bon
 
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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
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Old 2012-01-15, 16:55   #66
science_man_88
 
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Quote:
Originally Posted by schickel View Post
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 .
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