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I was playing around with various sets of numbers while thinking about optimizing neural networks and was wondering if numbers derived as below have a specific name

given a set: [7, 5, 3, 8, 1, 5]

the difference set is [-2, -2, 5, -7, 4]

the difference set for that is [0, 7, -12, 11]

the difference set for that is [7, -19, 23]

the difference set for that is [-26, 42]

the difference set for that is [68]

What is the mathematical term/name for '68' in this construct? I'm calling it the 'root differential' , but was sure somebody has already come up with one.

As a sort of side note, I found that the count of these roots can be found with the following

For integer sets of width W > 0 and max value W, there are a finite number of unique 'roots' which can be found by: roots = (w - 1) * 2^(w - 1) + 1 (Cullen numbers)

For integer sets of width W > 0 and max value M there are a finite number of unique 'roots' which can be found by: roots = (w - 1) * 2^(M - 1) + 1 (Proth numbers)

I'm mostly interested in the correct name for my 'root differentials'.

Thanks for any help

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# B Do numbers derived from successive differences have a name?

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