do  --[[ show members of the van der Corput sequence in various bases
         translated from the C sample
      ]]

    local int = require( "int" )                       -- RC integer module - includes gcd

    -- returns the numerator and denominator of the nth member of the van der Corput sequence
    -- in the specified base
    local function vc( nth : number, base : number )
        local p, q, n = 0, 1, nth

        while n != 0 do
            p  *= base
            p  += n % base
            q  *= base
            n //= base
        end

        num, denom = p, q

        -- return the numerator and denominator reduced by their gcd
        q = int.gcd( num, denom )
        return num // q, denom // q
    end

    -- task
    for b = 2, 5 do
        io.write( $"base {b}:" )
        for i = 0, 9 do
            local n, d = vc( i, b )
            io.write( if n != 0 then $"  {n}/{d}" else "  0" end )
        end
        io.write( "\n" )
    end
end