Use Part to make a list of the first 50 digits of 2^1000, in which each digit has a size equal to 3 times its value. can u give solution to this question!

Note to study group participants:

I've uploaded a new version of the Review notebook with corrections for a few typos and missing things. Please find it at the same folder!

I've also added the "Hamiltonian Mechanics" Manipulate example notebook that I showed, for the interested reader.

Lastly, I found the function I was looking for that can find generating functions for particular integer sequences—it's the rather obviously-named, in retrospect, FindSequenceFunction. I did scroll past it in the documentation when we were looking for it, but just glossed over it. It's neat!

# represents an arbitrary input without making explicit reference to a dummy variable like u or x. Except for in some very particular edge cases where you're nesting pure anonymous functions and can get into ambiguities about which slot is being referred to, it is exactly the same as Function[u,3+u] (which is also equal to Function[3+#]).

Do you have some particular use case in mind where these are not equivalent? If so, could you provide some more information?

Hi Mitch—the abbreviated form is what I stated above. Are you looking for a way to convert what you've written into that abbreviated form? If so, I'm not sure that there's a "native" way to do that, but you also shouldn't need to do that because these are functions that you write from scratch anyway, so you would just choose the format you wanted when writing them for the first time.

Here's a hacky solution that I've come up with; I can't guarantee that it works in 100% of cases: converter[func_] := (Evaluate[func[[2]] /. func[[1]] -> #]) & It extracts the "function" part of the Function, then replaces the "variable" part with a Slot[1] (#). The "Evaluate" is to make this operation actually evaluate, because by default it's taking the right-hand side as a pure function per se and thus not evaluating it. Then, I put a & at the end of this replaced version to close off the newly-made pure anonymous function.

I am intrigued but confused by RemoteBatch.
There is a lack of relevant topics and content in the community and document center.
Could Wolfram U consider offering some courses?

This is great news!