local fmt = require "fmt"

local limits = {
    range(3, 10), range(11, 18), range(19, 36),
    range(37, 54), range(55, 86), range(87, 118)
}

local function periodic_table(n)
    if n < 1 or n > 118 then error("Atomic number is out of range.") end
    if n == 1 then return {1, 1} end
    if n == 2 then return {1, 18} end
    if 57 <= n <= 71 then  return {8, n - 53} end
    if 89 <= n <= 103 then return {9, n - 85} end
    local row
    local start
    local finish
    for i = 1, #limits do
        local limit = limits[i]
        if limit[1] <= n <= limit:back() then
            row = i + 1
            start = limit[1]
            finish = limit:back()
            break
        end
    end
    if n < start + 2 or row == 4 or row == 5 then return {row, n - start + 1} end
    return {row, n - finish + 18}
end

for {1, 2, 29, 42, 57, 58, 59, 71, 72, 89, 90, 103, 113} as n do
    local rc = periodic_table(n)
    fmt.print("Atomic number %3d -> %d, %-2d", n, rc[1], rc[2])
end