do --[[ Find Mian-Chowla numbers: an
                           where: ai = 1,
                             and: an = smallest integer such that ai + aj is unique
                                                   for all i, j in 1 .. n && i <= j
     ]]
    local fmt = require( "fmt" )

    local maxMc, mcCount, mc, isSum = 100, 1, {}, {}
    local i = 0
    while mcCount <= maxMc do
        ++ i
        -- assume i will be part of the sequence
        mc[ mcCount ]  = i
        -- check the sums
        local isUnique = true
        for mcPos = 1, mcCount do
            if isSum[ i + mc[ mcPos ] ] then
                isUnique = false
                break
            end
        end
        if isUnique then
            -- i is a sequence element - store the sums
            for k = 1, mcCount do isSum[ i + mc[ k ] ] = true end
            ++ mcCount
        end
    end

    -- print parts of the sequence
    io.write( "Mian Chowla sequence elements 1..30:\n " )
    fmt.lprint( table.slice( mc, 1, 30 ),  " ", "" )
    io.write( "Mian Chowla sequence elements 91..100:\n " )
    fmt.lprint( table.slice( mc, 91, 100 ), " ", "" )

end