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I have an ordinal list that I am trying to represent mathematically. The list is as follows:

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000.

So basically, 100, 1000 and 10000 are multiplied by 10. I am visualising a chunk of data and I need an easy way to communicate the distribution without resorting to log. I'd like to formalise this, however.

cheers all,


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I removed the tag (ordinals) since this has nothing to do with ordinals (which is a well defined concept in set theory); I feel that there should be another tag brought in here, possibly to replace (problem-solving) altogether - however I'm not sure which tag fits. –  Asaf Karagila Apr 13 '11 at 14:16
You could consider generating functions. They would help you get a formula for the $n$th item in the list, and give a mathematical structure that contains the list. –  Matt Groff Apr 13 '11 at 14:32

2 Answers 2

See OEIS sequence A037124: Numbers that contain only one nonzero digit.

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which has the formula a(n) = [(n mod 9)+1] * 10^floor(n/9) and slotishtype wants the first 37 terms. –  Henry Apr 13 '11 at 15:17
@slotishtype: For your list (containing 37 terms) use the above formula for $n=9,10,\ldots,45$. –  Shai Covo Apr 13 '11 at 15:48

If the list stops at $100,000$, you have represented it by listing it. You could say something like $k10^n$ where $k \in \{1,2,3,4,5,6,7,8,9\}$ and $1 \le n \le 4$, but that is pretty complicated and leaves off the last term.

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Thanks Ross...I was just looking for some short hand notation but I am probably over complicating the issue... –  slotishtype Apr 13 '11 at 14:20

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