[QUOTE=VBCurtis;442233]Why not edit it now? I vote for a temporary ban if he continues to use white text. Not acceptable.[/QUOTE]

Mainly because I was busy. Handing my dissertation in tomorrow. I may got back and edit that one when I have time.

[QUOTE=mshelikoff;442239]I'm still writing about this topic after I wrote "nevermind," so I apologize for writing "nevermind" because obviously I'm still thinking about it, and I'm fairly new to the forum and might be making a mistake by asking this question now. But...

What are the odds of this sequence meeting itself and creating a very large cycle if the sequence dips below a given number of digits (I'll use 7) and then terminates? Maybe it's an unlikely precondition before even considering the chances of the event if the precondition takes place. But I'm curious about it and wondering if I'm thinking about it the right way. I'm not talking about when a merger is found but how the final sequence at factordb will appear.

If the count of non-untouchable numbers above 10^7 with an immediate descendant below 10^7 were used as a denominator and the count of the subset of those numbers that belong to the 4788 genealogy were used as the numerator, would that fraction give a reasonable estimate of the odds?

I'm using the word "odds" as if this were a horse race instead of the given fixed probabilities in Raman's post, but that seems to be part of the appeal of following these things.[/QUOTE]
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.

In step 6295 it reached:
108779027694592579666495916767464 (33 digits)

and then it went up again. Now it is back to 88 digits in step 6666.

And now we're going down again, as of terms 6700 onward...

got down as low s 18 digits, now it went up to 70 digits

[QUOTE=firejuggler;442249]i 7200-7300 it's hovering around 20-25 digits[/QUOTE]

and at 7581 it's back up to over 60. edit: and moving so fast I can't keep this up to date 7639 and 71 digits now edit2: changed already.

Minimum at 16 digits and now it grows with 2^2*7 driver.

It looks like it picked up a 2^2·7 at the 16 digit 1987170707261684 , found the downdriver later, and then picked up another 2^2·7 at 20 digits and this one isn't leaving.

This is almost heartbreaking.

Just as heartbreaking as [URL="http://factordb.com/sequences.php?se=1&aq=4788&action=range&fr=3925&to=3999"]the previous bottom[/URL].
But then again look at AllSeq page - there are constantly 30-40 downdrivers but only 1 per few months terminations/merges...

Not all is lost just yet!

Minimum was step 7189:
1987170707261684 (16 digits)