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Old 2014-03-05, 17:42   #1
ChristianB
 
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Default Sequences using nine-digit pandigital numbers as start

I recently started to compute aliquot sequences using nine-digit pandigital numbers as input. I'm no mathematician and there is no goal in this other than factoring numbers. I already set up a little toolchain that goes through all permutations of 123456789 and computes the aliquot sequence using aliqueit. Of course I check with factordb before and after.

The current goal is to filter out all the sequences that end with a prime or merge into a sequence that ends and bring the remaining ones to at least C80 (cofactor size). I don't know yet if there is something specific to look for but I plan to find a pandigital sequence that merges into another pandigital sequence.

I don't know if you find that interesting, for me it is.
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Old 2014-03-05, 19:57   #2
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Do not start any odd-sequence , it can only drop go down, or stay the same number if it is prime.

Last fiddled with by firejuggler on 2014-03-05 at 19:59
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Old 2014-03-05, 20:04   #3
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Quote:
Originally Posted by firejuggler View Post
Do not start any odd-sequence , it can only drop go down, or stay the same number if it is prime.

http://oeis.org/A005231

While they're much less common than even ones, there is such a thing as an odd abundant number.
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Old 2014-03-05, 20:17   #4
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ah.. then amend it to 'Do not start any odd-sequence , it can only go down, or be really short'
To be honest, I have never heard of ' odd abundant number'. Does a pan-digital one exist?

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Old 2014-03-05, 20:24   #5
Batalov
 
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Quote:
Originally Posted by firejuggler View Post
Do not start any odd-sequence , it can only drop go down, or stay the same number if it is prime.
Not necessarily. And not even necessarily they will end really fast.

For example, look at 123578469 or 123584697 or 124859367 or 126794583 or 126857439 or ...
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Old 2014-03-05, 20:30   #6
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Ok then, ignore my previous comment... But don't forget that the OP did want to avoid merges.
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Old 2014-03-05, 20:37   #7
ChristianB
 
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Quote:
Originally Posted by firejuggler View Post
Do not start any odd-sequence , it can only drop go down, or stay the same number if it is prime.
So what about these sequences:
123578469 merging into 99225
123584697 merging into 1098

So far those are the only odd ones that are not ending in a prime. I will keep running the odd ones for some time to see if there are more.

Edit: Batalov was faster than me. I don't want to avoid merges, at the moment I only detect them and keep computing later.

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Old 2014-03-05, 21:48   #8
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Another bit of info, then : if the sequence fall below 1'000'000 or 1M, it has been pushed beyond 80 digits... 120 digits, if my memory serve.
Look at rieselprime.de

Last fiddled with by firejuggler on 2014-03-05 at 22:01
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Old 2014-03-05, 21:48   #9
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Quote:
Originally Posted by firejuggler View Post
Does a pan-digital one exist?
There are 5799 odd abundant pan-digital numbers. (out of 201600 of this 1-9 kind)

There are 47016 odd abundant pan-ten-digital numbers. (out of 1612800 of the ten-digit 0-9 kind)
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Old 2014-03-06, 08:05   #10
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Quote:
Originally Posted by firejuggler View Post
Another bit of info, then : if the sequence fall below 1'000'000 or 1M, it has been pushed beyond 80 digits... 120 digits, if my memory serve.
Look at rieselprime.de
As I understand aliqueit, it does detect such a case. I then upload the sequence to factordb and redownload the new one. If the cofactor is above C80 I try the next pandigital. From time to time I check the factordb on the latest index and what cofactor it has. In a second stage I'm going to advance those further.
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Old 2014-03-07, 08:35   #11
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Some work:

There're 362880 combinations for digits 1-9, 9 digits long.

odd : 201600
even: 161280

For the first 5700 odd seqs (beginning with 123456789 up to 143829675) there're these seqs open ended and merging with lower open seqs:

123578469 -> 46758
123584697, 124859367 -> 448476
126794583 -> 259320
126857439 -> 442962
128653479 -> 273540
128974635 -> 2982
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