This numeral system is utterly obscure, and seems to have no use at all anywhere. So, is there any formal or scientific use for a base $7$ numeral system anywhere?
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Can't think of any as such. And what's the relation between the representation you created to the question? "1,2,3,4,.." was adopted just because its easy to write, doesn't matter even if you write "I,II,III.. " (or what you "developed") instead of it, long as the meaning is conveyed to the ones in receiving end. – Jesse P Francis Apr 24 '15 at 09:26
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Prime based number systems have some special use. P.ex. see p-adic systems. If you are interested in strange-based systems then take a look at: http://hsm.stackexchange.com/questions/2181/has-a-digit-ever-been-used-to-represent-the-number-10/2211#2211 – zoli Apr 24 '15 at 09:34
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2Yes, in hexagonal image processing, but I'm not familiar with the details. – Chris Culter Apr 24 '15 at 09:49