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A curious math problem I came up with: given a target, what's the fewest digits an integer must have (in a given base) to contain all integers from 0 to the target, as substrings? (sociale.network)

submitted 6 months ago* (last edited 6 months ago) by [email protected] to c/[email protected]

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A curious math problem I came up with: given a target, what's the fewest digits an integer must have (in a given base) to contain all integers from 0 to the target, as substrings?

http://wok.oblomov.eu/mathesis/number-substrings/

@mathematics @[email protected] @[email protected]

e.g. for a target of 19 a candidate representative would be 1011213141516171819 in base 10, that has 19 digits. Can it be done in less, or is $\sigma_10(19) = 19$?
Can we find a general rule? Any properties of this function?

#math #maths #numberTheory #combinatorics

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[–] [email protected] 1 points 6 months ago

@TootSweet this reminds me of https://github.com/philipl/pifs, the filesystem based on the normality of π