[QUOTE=henryzz;442244]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.[/QUOTE]

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.

[QUOTE=mshelikoff;442262]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.[/QUOTE]

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.

And there, 2^2 * 7^2 in i7825 with proper two primes (1 mod 4), and 2^2 * 7 is lost!

Uh oh. And now factordb appears to be down. Did I break it? :sad:

can we get an update on the status on 4788 since factordb is down?

[QUOTE=ryanp;442280]Uh oh. And now factordb appears to be down. Did I break it? :sad:[/QUOTE]

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 :smile:

grrrr... 2^2*7, I told you that you are jinxing it! A fisherman never counts his fish! :razz:
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.

Status
[CODE]n Digits Number
7926 121 [URL="http://factordb.com/index.php?showid=1100000000866145455"](show)[/URL] [URL="http://factordb.com/index.php?id=1100000000866145455"]3936113967...80[/URL]<121> = 2^2 · 5 · 3163 · 11273 · [URL="http://factordb.com/index.php?id=1100000000866145457"]5519490243...71[/URL]<112>[/CODE]

[QUOTE=Batalov;442287]Status
[CODE]n Digits Number
7926 121 [URL="http://factordb.com/index.php?showid=1100000000866145455"](show)[/URL] [URL="http://factordb.com/index.php?id=1100000000866145455"]3936113967...80[/URL]<121> = 2^2 · 5 · 3163 · 11273 · [URL="http://factordb.com/index.php?id=1100000000866145457"]5519490243...71[/URL]<112>[/CODE][/QUOTE]That's 16 more lines than I have. Maybe we can get lucky again!

The easiest way to picture it is [URL="http://factordb.com/aliquot.php?type=1&aq=4788"]the graph[/URL].

Obviously the x-axis is iterations rather than time, so much less time is spent at low levels of y.

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!