require "table2"
local int = require "int"
local fmt = require "fmt"

local limit = 100
local starts = {2, 5, 7, 9, 10}
local ekg = {}
for i = 1, 5 do ekg[i] = table.rep(limit, 0) end
local s = 1
for starts as start do
    ekg[s][1] = 1
    ekg[s][2] = start
    for n = 3, limit do
        local i = 2
        while true do
            -- A potential sequence member cannot already have been used
            -- and must have a factor in common with previous member.
            if !ekg[s]:slice(1, n):contains(i) and int.gcd(ekg[s][n - 1], i) > 1 then
                ekg[s][n] = i
                break
            end
            i += 1
        end
    end
    fmt.write("EKG(%2d): ", start)
    fmt.tprint("%2d", ekg[s]:slice(1, 30), 30)
    s += 1
end

-- Now compare EKG5 and EKG7 for convergence.
for i = 3, limit do
    if ekg[2][i] == ekg[3][i] and
       table.same(ekg[2]:slice(1, i - 1):sort(), ekg[3]:slice(1, i - 1):sort()) then
        print($"\nEKG(5) and EKG(7) converge at term {i}.")
        os.exit()
    end
end
print($"\nEKG5(5) and EKG(7) do not converge within {limit} terms.")