20-109 - each digit is used 19 times. 200-1099 - each digit is used 280 times 2000-10999 - each digit is used 3700 times 20000-109999 - each digit used 46000 times. In fact, it looks like the range from 2x10^n to 11x10^n - 1 (n = 0, 1, 2, 3...) will have the desired property. 2 followed by n 0s ... 10 followed by (n-1) 9s uses each digit OEIS A081045 number of times David P Stigant, Kirk Bresniker, Doron Osovlanski, Nathan Stohler, Joseph DeVincentis The Following Sequence uses all the digits six times: 12233445566778890999, 12233445566778891000, 12233445566778891001. -Arthur Drehman The following range, for any n, seems to use each of the digits from 0 to 9 exactly the same number of times: 2*(10^n) <= k < 11*(10^n) The example that Bernardo provides is the set for n=0. Are there any sequences that are substantially different from this category? Kenny Young 10234567890 10234567891 10234567892 10234567893 10234567894 10234567895 10234567896 10234567897 10234567898 10234567899 In general, let N be a single integer that contains each digit (0-9) k times. Then (10N+0, 10N+1, ..., 10N+9) is a nicely distributed sequence of multiplicity 10k+1. The given sequence is the one with the smallest value of N in this family. Juha Saukkola, Clinton Weaver, Robert Wainwright, Heinrich Hemme, Jonathan Fero, Corey Maley, Luke Pebody, Siva Naga Prasad Sajja, Bob Kraus, maurizio codogno, Joseph DeVincentis, Steve Amato