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Old 2020-09-02, 19:23   #538
garambois's Avatar
"Garambois Jean-Luc"
Oct 2011

10101001112 Posts

Originally Posted by EdH View Post
Ah, so we need even terms for it to be open, as well, because odd terms will eventually descend?

I won't hold that against you. I might even move back that way myself. But, currently, we seem to be displaying a lot of evidence for terminations.

In fact, I don't really know what we should consider an Open-End sequence. But I do make two observations :

1) In the main project, on the blue page, I've never seen an Open-End sequence that starts on an odd number. But maybe there is one and I don't know how to filter it ?

2) On all the aliquots sequences that start on integers from 1 to 10,000,000, thanks to my fundamental database, I know that the absolute record for a growth sequence with consecutive odd terms is held by the sequence that starts on the integer 2,551,185. And this number of growing consecutive terms is only 6, which is very little. (see here some other records)

Having made these two observations, I tell myself that a sequence can only be Open-End with even terms for numbers of a few hundred digits that we work with.
But maybe it should also be possible to have an Open-End sequence with huge odd terms. But discovering such odd Open-End sequences (if they exist) is far from being within our reach.
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