Mathematics

502 readers

1 users here now

A community for discussing mathematics and developments in mathematics.

founded 3 years ago

MODERATORS

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 8 months ago* (last edited 8 months ago) by oblomov@sociale.network to c/mathematics@lemmy.ml

6 comments fedilink hide all child comments

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 @math@lemmy.ml @math@kbin.social

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

you are viewing a single comment's thread
view the rest of the comments

[–] oblomov@sociale.network 1 points 8 months ago

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