do  -- Rare numbers - translation of EasyLang with the MOD 1089/121 test from FreeBASIC

    local function rev( n )
        local h, r = n, 0
        while h > 0 do
            r = r * 10 + h % 10
            h = math.floor( h / 10 )
        end
        return r
    end

    local function issqr( n )
        local h = math.sqrt( n )
        return math.floor( h ) == h
    end

    local po, oddDigits, lim, a, count, n = 1, true, 1, 0, 0, 0

    while count < 5 do
        n = n + 1
        if n == lim then
            a = a + 2
            if a == 10 then
                a         = 2
                po        = po * 10
                oddDigits = not oddDigits
            end
            n   = a * po
            lim = n + po
        end
        local q = n % 10
        if a ~= 2 or q == 2 then
            if a ~= 4 or q == 0 then
                if a ~= 6 or q == 0 or q == 5 then
                    local s9 = ( n % 9 * 2 ) % 9
                    if s9 <= 1 or s9 == 4 or s9 == 7 then
                        if q ~= 1 and q ~= 4 and q ~= 6 and q ~= 9 then
                            local h = a - q
                            if h <= 1 or h >= 4 and h <= 6 then
                                local nrev = rev( n )
                                if n > nrev then
                                    local s, d = n + nrev, n - nrev
                                    if  (   oddDigits
                                        and d % 1089 == 0
                                        or  s %  121 == 0
                                        )
                                    then
                                        if issqr( s ) then
                                            if issqr( d ) then
                                                io.write( " "..n )
                                                count = count + 1
                                            end
                                        end
                                    end
                                end
                            end
                        end
                    end
                end
            end
        end
    end
end