It's not clear if this is exactly what you're looking for. Do the starting values all need to be multiples of 0.02 as well? If so, these are the 9 possible sets that match your brief.
lapply(seq(0.5, 0.66, 0.02), function(x) x + 0.02*0:4)
#> [[1]]
#> [1] 0.50 0.52 0.54 0.56 0.58
#>
#> [[2]]
#> [1] 0.52 0.54 0.56 0.58 0.60
#>
#> [[3]]
#> [1] 0.54 0.56 0.58 0.60 0.62
#>
#> [[4]]
#> [1] 0.56 0.58 0.60 0.62 0.64
#>
#> [[5]]
#> [1] 0.58 0.60 0.62 0.64 0.66
#>
#> [[6]]
#> [1] 0.60 0.62 0.64 0.66 0.68
#>
#> [[7]]
#> [1] 0.62 0.64 0.66 0.68 0.70
#>
#> [[8]]
#> [1] 0.64 0.66 0.68 0.70 0.72
#>
#> [[9]]
#> [1] 0.66 0.68 0.70 0.72 0.74
If the starting numbers can take any value, then a better solution would be
runif(1, 0.5, 0.67) + 0.02 * 0:4
Which you can put into a loop or lapply
to get any number of samples like this:
lapply(seq(5), function(x) runif(1, 0.5, 0.67) + 0.02 * 0:4)
#> [[1]]
#> [1] 0.5973477 0.6173477 0.6373477 0.6573477 0.6773477
#>
#> [[2]]
#> [1] 0.5174972 0.5374972 0.5574972 0.5774972 0.5974972
#>
#> [[3]]
#> [1] 0.6529702 0.6729702 0.6929702 0.7129702 0.7329702
#>
#> [[4]]
#> [1] 0.5418349 0.5618349 0.5818349 0.6018349 0.6218349
#>
#> [[5]]
#> [1] 0.5071501 0.5271501 0.5471501 0.5671501 0.5871501