Values from the real-valued sequence R = {1.0, 1.25, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0, 6.0, 8.0, 10.0, 12.5, 15.0, 20.0, 25.0, 30.0, 40.0, 50.0, 60.0, 80.0, 100.0, 125.0, 150.0, 200.0, 250.0, 300.0, 400.0, 500.0, 600.0, 800.0, 1000.0, ...} are used in certain computer applications, such as geographic information system (GIS) applications where they are provided as round numbers for selection as map scale values. This real-valued sequence R (all of whose values above 12.5 are integers) represents a convenient balance between roundness of the base-10 values and evenness of their spacing (in logarithmic terms).
The real-valued sequence can be continued infinitely in both directions; for simplicity, the terms listed in the Data section for this integer sequence begin at a(20) = 100 = 10^2. (Extending the sequence to lower values of n would cause the noninteger value 12.5 to be reached at n=11.)
Some properties of the sequence (see Example section):
(1) on a logarithmic scale, the terms are fairly evenly spaced;
(2) all terms are round numbers; other than those terms that begin with digits 125, 15, or 25 (each of which has no prime factor larger than 5), each term has only one nonzero digit;
(3) there are 10 terms per order of magnitude;
(4) every ratio between consecutive terms is one of three small fractions: 4/3, 5/4, and 6/5.
