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2020-08-10, 16:39   #398
garambois

Oct 2011

22·3·29 Posts

Quote:
 Originally Posted by EdH I look forward to seeing all the colors! Are there more data points for consideration? A couple things interesting to me: 1. ATM, 2^544 has a "3" downdriver. 2. 2^543 shed 69 digits from index 9 to index 10 (151-82 dd).

Unfortunately, I have not yet had the time to study this aspect of the sequences for the different bases. But I note these remarks for some time to come when I will start this kind of studies...
I am working very intensively on prime numbers and their occurrence in the different sequences and it takes all my time.
I finally have the right analysis programs. And everything corresponds perfectly to the results of EdH !
I think I will be able to present you with several new conjectures in the next few days, but before I do, I'd rather check them out.
I will take some time to update the page very soon. So I have a question for Ed :
@EdH : I understand you're working on the 2^i sequences with i>540. Should I add a line from 2^540 to 559 ?
Otherwise, if possible the first priority would be to compute the first 4 indexes of the sequences 2^(36*k), 2^(60*k), 2^(70*k), with k integer and the first 3 indexes of the sequences 2^(70*k), 2^(72*k), 2^(90*k), with k integer and of course 36*k>540, 60*k>540, 70*k>540... (because when it's <540, we've already got them !)
This has something to do with the conjectures I will be stating in a few days.
For example, I observe that the prime number 5 is found in the decompositions of terms at indexes 1 to 4 of sequences that begin with 2^(36*k) or that the prime number 19 is found in the decompositions of terms at indexes 1 to 3 of sequences that begin with 2^(72*k). But I think that this must stop after a certain rank, so I would like to prove it...