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A292275 A sequence of rounded numbers useful for entering values over several orders of magnitude in computer-human interfaces, with 10 values per order of magnitude. 0
100, 125, 150, 200, 250, 300, 400, 500, 600, 800, 1000, 1250, 1500, 2000, 2500, 3000, 4000, 5000, 6000, 8000, 10000, 12500, 15000, 20000, 25000, 30000, 40000, 50000, 60000, 80000, 100000, 125000, 150000, 200000, 250000, 300000, 400000, 500000, 600000, 800000, 1000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

20,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=20..60.

FORMULA

a(n) = 10^n *  1  if n mod 10 = 0;

       10^n * 5/4 if n mod 10 = 1;

       10^n * 3/2 if n mod 10 = 2;

       10^n *  2  if n mod 10 = 3;

       10^n * 5/2 if n mod 10 = 4;

       10^n *  3  if n mod 10 = 5;

       10^n *  4  if n mod 10 = 6;

       10^n *  5  if n mod 10 = 7;

       10^n *  6  if n mod 10 = 8;

       10^n *  8  if n mod 10 = 9.

EXAMPLE

n   a(n)  a(n)/a(n-1)   log_10(a(n))    log_10(a(n)) - n/10

==  ====  ===========  ===============  ===================

20   100      5/4      2.0000000000...   0.0000000000000...

21   125      5/4      2.0969100130...  -0.0030899869919...

22   150      6/5      2.1760912590...  -0.0239087409443...

23   200      4/3      2.3010299956...  +0.0010299956639...

24   250      5/4      2.3979400086...  -0.0020599913279...

25   300      6/5      2.4771212547...  -0.0228787452803...

26   400      4/3      2.6020599913...  +0.0020599913279...

27   500      5/4      2.6989700043...  -0.0010299956639...

28   600      6/5      2.7781512503...  -0.0218487496163...

29   800      4/3      2.9030899869...  +0.0030899869919...

30  1000      5/4      3.0000000000...   0.0000000000000...

CROSSREFS

Cf. A231848.

Sequence in context: A066139 A037139 A109881 * A295161 A127336 A045211

Adjacent sequences:  A292272 A292273 A292274 * A292276 A292277 A292278

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Sep 12 2017

STATUS

approved

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Last modified March 26 23:07 EDT 2019. Contains 321566 sequences. (Running on oeis4.)