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What common property unites all of the following numbers?

4, 9, 60, 101, 400, 450, 910, 1010

The set of numbers that share this common property is not limited to just these eight, but the list should provide enough information to solve it.

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  • $\begingroup$ Can we also assume that no other numbers below 1010 share this commonality? $\endgroup$
    – breadbox
    Commented Mar 13, 2015 at 3:16
  • $\begingroup$ @breadbox I didn't find any more below 1010 but there could have been some that I missed $\endgroup$
    – Ben
    Commented Mar 13, 2015 at 3:50

2 Answers 2

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There are the numbers whose roman numeral translations are in strict alphabetical order (so no repetitions).
4=IV, 9=IX, 60=LX, 101=CI, 400=CD, 450=CDL, 910=CMX, 1010=MX

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  • $\begingroup$ If this is correct, then there's also 104, 109, 401, 404, 409, 501, 504, 509, 550, 905, and 1005. $\endgroup$
    – breadbox
    Commented Mar 13, 2015 at 4:59
  • $\begingroup$ You're right, those ones fit too. I wasn't sure if putting a lot of numbers would give it away too quickly so I stopped once I had found 8 :) $\endgroup$
    – Ben
    Commented Mar 13, 2015 at 13:49
  • $\begingroup$ If you take out 450 and 910 from the original list, you get a tighter pattern that also includes 501, 505, 550, 900, 1005, ... $\endgroup$ Commented Oct 8, 2015 at 15:38
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I guess it is

Roman numerals with 1 letter, in alphabetical order; then those with 2 letters, etc.

and the source is http://oeis.org/A003588

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