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User:S. Brunner

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Amateur mathematican from Germany.

I earn my bread with manual work, but I'm very interested in doing calculations, programming and building complicated Excel spreadsheets as a hobby.

A few years ago I made the observation that you can get all fractions between 1 and 1 + sqrt of 2 without duplicates from the primitive Pythagorian triangles and submitted it as the sequences A328972/A328973. I'm very curios why exactly you get this fractions and could not figure out what properties of the primitive Pythagorian triangles exactly cause this. Although I didn't find any mention of this fractions anywhere on the internet. So if someone more knowledgeable than me has figured it out and could it explain in detail I would be very satisfied.

I have another sequence in work, which would need at least another term to be submitted. I want to count the number of distinct paperfolds you can produce from a square piece of paper with n folds. Paperfolds are distinct when they have an unique order of paper layers and an unique connection between the paper layers at the folds and can not turned into another paperfold by turning it upside down. The sequence starts with 1,1,5,? The 5 different paperstacks with 2 folds are: 4 layers: - Fold top to bottom, fold top to bottom again. - Fold top to bottom, fold left to right. 3 layers: - Fold top quarter down, fold back top to bottom. (like a paper fan) - Fold top quarter down, fold top to bottom. (paper roll) 2 layers: - Fold top quarter down, fold bottom quarter up (tablet)

For n=3 I started counting but I found it to complicated and lost time and interest for it. I estimate a(3) to be 60-100.

So if someone has a program or an idea to systematically count all paperfolds please contact me.