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Old 2016-09-11, 21:37   #2575
mshelikoff
 
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Quote:
Originally Posted by henryzz View Post
I think that this is an incredibly hard question to answer. I think that each number has a different number of numbers that can precede it. This implies to me that it is not a simple formula as 4788 has a certain subset of the numbers below 10^7. I think that working this out would be exceedingly difficult.
Working out all the numbers that can precede a number in a sequence is not easy.
If the number of sequence transitions from above to below 10^7 (instead of the numbers below 10^7) were considered in the 4788 genealogy compared to all such transitions then wouldn't that roughly account for the different number of numbers that can precede a number in a sequence? I don't know if that would be a way to get an order-of-magnitude estimate.

Further edit: Maybe 10^7 is too large because the numbers that precede would need to be worked out. A smaller 10^n might be able to test the idea of whether it estimates the likelihood of a much greater number falling into a certain genealogy.

Last fiddled with by mshelikoff on 2016-09-11 at 21:45 Reason: Considered precedents to 10^n instead of 10^7
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Old 2016-09-11, 21:48   #2576
science_man_88
 
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Quote:
Originally Posted by mshelikoff View Post
If the number of sequence transitions from above to below 10^7 (instead of the numbers below 10^7) were considered in the 4788 genealogy compared to all such transitions then wouldn't that roughly account for the different number of numbers that can precede a number in a sequence? I don't know if that would be a way to get an order-of-magnitude estimate.
the problem is it depends on what you mean by transitions below did you know that because 4787 is prime that 4787^2 leads to 4788 ? that number is over 22 million. and that's not on the linked genealogy to my knowledge of what you said so any that branch back from that number will also lead to 4788. the number of numbers that can precede a number in a sequence is the number of partitions that are a proper divisors list for another number.

E.g. 6 = 1+5 = 1+2+3 are the only possible arrangements using 1 as the start ( a necessity to be a divisors list) this leads to 25 and 6 being the numbers that can get to 6. 6 has been repeated so let's check 25 and we get:

95
119
143

but that would have started with something like 66 possible partitions that have strictly increasing members starting at 1 that could ( before inspection further) possibly have lead to 25.

Last fiddled with by science_man_88 on 2016-09-11 at 22:01
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Old 2016-09-11, 22:06   #2577
Batalov
 
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And there, 2^2 * 7^2 in i7825 with proper two primes (1 mod 4), and 2^2 * 7 is lost!
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Old 2016-09-12, 04:58   #2578
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Uh oh. And now factordb appears to be down. Did I break it?
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Old 2016-09-12, 05:06   #2579
firejuggler
 
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can we get an update on the status on 4788 since factordb is down?
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Old 2016-09-12, 05:34   #2580
rajula
 
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Quote:
Originally Posted by ryanp View Post
Uh oh. And now factordb appears to be down. Did I break it?
It is probable that your work attracted too much interest and people were refreshing the page very frequently. Maybe just continue off-line and keep us updated
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Old 2016-09-12, 05:40   #2581
LaurV
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grrrr... 2^2*7, I told you that you are jinxing it! A fisherman never counts his fish!
OTOH, D2 is a "good driver", with only a mild increase (compared with D3 or others).

P.S., FDB seems down from this part of the world too.
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Old 2016-09-12, 06:54   #2582
Batalov
 
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Status
Code:
n    Digits     Number 
7926 121 (show) 3936113967...80<121> = 2^2 · 5 · 3163 · 11273 · 5519490243...71<112>
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Old 2016-09-12, 07:05   #2583
schickel
 
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Quote:
Originally Posted by Batalov View Post
Status
Code:
n    Digits     Number 
7926 121 (show) 3936113967...80<121> = 2^2 · 5 · 3163 · 11273 · 5519490243...71<112>
That's 16 more lines than I have. Maybe we can get lucky again!
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Old 2016-09-12, 08:21   #2584
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The easiest way to picture it is the graph.

Obviously the x-axis is iterations rather than time, so much less time is spent at low levels of y.
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Old 2016-09-12, 09:56   #2585
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4788 has become the 8th longest open Aliquot sequence below 1e6, and it has all the chances to become 6th in the near future. However if we take merges into account then the sequence 314718 with currently 14420 terms has become the longest Aliquot sequence below 1e6.
Great job!
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