How to generate a n numbers with equal intervals in a specific range using R

If I understand you correctly, you want a series of 100 numbers starting at 0.001 and ending at 1000, where the ratio between consecutive numbers is fixed. You can get this with:

x <- 10^seq(log10(0.001), log10(1000), length = 100)

x
#>   [1] 1.000000e-03 1.149757e-03 1.321941e-03 1.519911e-03 1.747528e-03
#>   [6] 2.009233e-03 2.310130e-03 2.656088e-03 3.053856e-03 3.511192e-03
#>  [11] 4.037017e-03 4.641589e-03 5.336699e-03 6.135907e-03 7.054802e-03
#>  [16] 8.111308e-03 9.326033e-03 1.072267e-02 1.232847e-02 1.417474e-02
#>  [21] 1.629751e-02 1.873817e-02 2.154435e-02 2.477076e-02 2.848036e-02
#>  [26] 3.274549e-02 3.764936e-02 4.328761e-02 4.977024e-02 5.722368e-02
#>  [31] 6.579332e-02 7.564633e-02 8.697490e-02 1.000000e-01 1.149757e-01
#>  [36] 1.321941e-01 1.519911e-01 1.747528e-01 2.009233e-01 2.310130e-01
#>  [41] 2.656088e-01 3.053856e-01 3.511192e-01 4.037017e-01 4.641589e-01
#>  [46] 5.336699e-01 6.135907e-01 7.054802e-01 8.111308e-01 9.326033e-01
#>  [51] 1.072267e+00 1.232847e+00 1.417474e+00 1.629751e+00 1.873817e+00
#>  [56] 2.154435e+00 2.477076e+00 2.848036e+00 3.274549e+00 3.764936e+00
#>  [61] 4.328761e+00 4.977024e+00 5.722368e+00 6.579332e+00 7.564633e+00
#>  [66] 8.697490e+00 1.000000e+01 1.149757e+01 1.321941e+01 1.519911e+01
#>  [71] 1.747528e+01 2.009233e+01 2.310130e+01 2.656088e+01 3.053856e+01
#>  [76] 3.511192e+01 4.037017e+01 4.641589e+01 5.336699e+01 6.135907e+01
#>  [81] 7.054802e+01 8.111308e+01 9.326033e+01 1.072267e+02 1.232847e+02
#>  [86] 1.417474e+02 1.629751e+02 1.873817e+02 2.154435e+02 2.477076e+02
#>  [91] 2.848036e+02 3.274549e+02 3.764936e+02 4.328761e+02 4.977024e+02
#>  [96] 5.722368e+02 6.579332e+02 7.564633e+02 8.697490e+02 1.000000e+03

Or, if you don't like scientific notation,

print(format(round(x, 5), drop0trailing = TRUE), quote = FALSE)
#>   [1]    0.001      0.00115    0.00132    0.00152    0.00175    0.00201
#>   [7]    0.00231    0.00266    0.00305    0.00351    0.00404    0.00464
#>  [13]    0.00534    0.00614    0.00705    0.00811    0.00933    0.01072
#>  [19]    0.01233    0.01417    0.0163     0.01874    0.02154    0.02477
#>  [25]    0.02848    0.03275    0.03765    0.04329    0.04977    0.05722
#>  [31]    0.06579    0.07565    0.08697    0.1        0.11498    0.13219
#>  [37]    0.15199    0.17475    0.20092    0.23101    0.26561    0.30539
#>  [43]    0.35112    0.4037     0.46416    0.53367    0.61359    0.70548
#>  [49]    0.81113    0.9326     1.07227    1.23285    1.41747    1.62975
#>  [55]    1.87382    2.15443    2.47708    2.84804    3.27455    3.76494
#>  [61]    4.32876    4.97702    5.72237    6.57933    7.56463    8.69749
#>  [67]   10         11.49757   13.21941   15.19911   17.47528   20.09233
#>  [73]   23.1013    26.56088   30.53856   35.11192   40.37017   46.41589
#>  [79]   53.36699   61.35907   70.54802   81.11308   93.26033  107.22672
#>  [85]  123.28467  141.74742  162.97508  187.38174  215.44347  247.70764
#>  [91]  284.80359  327.45492  376.49358  432.87613  497.70236  572.23677
#>  [97]  657.93322  756.46333  869.749   1000

Here, each number is 1.149757 times larger than the preceding number, as we csn see by doing:

sapply(1:99, function(i) x[i+1]/x[i])
#>  [1] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#>  [9] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [17] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [25] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [33] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [41] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [49] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [57] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [65] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [73] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [81] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [89] 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757 1.149757
#> [97] 1.149757 1.149757 1.149757

^{Created on 2022-08-28 with reprex v2.0.2}

• We can use the idea of Geometric Sequence with a the first term , b the last term and n the number of terms

geo_seq <- function(a , b , n){
    r <- (b/a)^(1/(n-1))
    sapply(1:n , \(x) a * r^(x-1))
}

geo_seq(.001 , 1000 , 7)

• Output

[1] 1.000000e-03 1.149757e-03 1.321941e-03 1.519911e-03
[5] 1.747528e-03 2.009233e-03 2.310130e-03 2.656088e-03
[9] 3.053856e-03 3.511192e-03 4.037017e-03 4.641589e-03
[13] 5.336699e-03 6.135907e-03 7.054802e-03 8.111308e-03
[17] 9.326033e-03 1.072267e-02 1.232847e-02 1.417474e-02
[21] 1.629751e-02 1.873817e-02 2.154435e-02 2.477076e-02
[25] 2.848036e-02 3.274549e-02 3.764936e-02 4.328761e-02
[29] 4.977024e-02 5.722368e-02 6.579332e-02 7.564633e-02
[33] 8.697490e-02 1.000000e-01 1.149757e-01 1.321941e-01
[37] 1.519911e-01 1.747528e-01 2.009233e-01 2.310130e-01
[41] 2.656088e-01 3.053856e-01 3.511192e-01 4.037017e-01
[45] 4.641589e-01 5.336699e-01 6.135907e-01 7.054802e-01
[49] 8.111308e-01 9.326033e-01 1.072267e+00 1.232847e+00
[53] 1.417474e+00 1.629751e+00 1.873817e+00 2.154435e+00
[57] 2.477076e+00 2.848036e+00 3.274549e+00 3.764936e+00
[61] 4.328761e+00 4.977024e+00 5.722368e+00 6.579332e+00
[65] 7.564633e+00 8.697490e+00 1.000000e+01 1.149757e+01
[69] 1.321941e+01 1.519911e+01 1.747528e+01 2.009233e+01
[73] 2.310130e+01 2.656088e+01 3.053856e+01 3.511192e+01
[77] 4.037017e+01 4.641589e+01 5.336699e+01 6.135907e+01
[81] 7.054802e+01 8.111308e+01 9.326033e+01 1.072267e+02
[85] 1.232847e+02 1.417474e+02 1.629751e+02 1.873817e+02
[89] 2.154435e+02 2.477076e+02 2.848036e+02 3.274549e+02
[93] 3.764936e+02 4.328761e+02 4.977024e+02 5.722368e+02
[97] 6.579332e+02 7.564633e+02 8.697490e+02 1.000000e+03