Module:Collatz sequence Generator

local p = {}

function p.collatz(frame)
    local n = tonumber(frame.args[1])  -- Input number
    if not n or n < 1 then
        return "Please provide a positive integer."
    end

    local bold = frame.args['bold']  -- Bold parameter
    local max = tonumber(frame.args['max'])  -- Maximum steps
    local display_steps = frame.args['steps'] == "yes"  -- Whether to display total steps
    local hide_sequence = frame.args['hide'] == "yes"  -- Whether to hide the sequence

    -- Check if both 'hide' and 'max' are set (conflict)
    if hide_sequence and max then
        return "Error: Sequence is hidden. Please remove the 'max' parameter."
    end

    local sequence, count = {}, 0  -- Initialize sequence and counter

    -- Helper to conditionally bold numbers
    local function maybe_bold(num)
        local result = tostring(num)
        if (num % 2 == 0 and bold == "even") or (num % 2 ~= 0 and bold == "odd") then
            return "'''" .. result .. "'''"  -- Bold even or odd numbers
        end
        return result  -- Return unbolded if condition not met
    end

    -- Function to handle the Collatz logic and format sequence
    local function collatz_step(num)
        table.insert(sequence, maybe_bold(num))
        count = count + 1  -- Increment step count
        return num % 2 == 0 and num / 2 or 3 * num + 1  -- Next Collatz step
    end

    -- Main Collatz loop
    while n > 1 do
        if max and count >= max then  -- Stop if max steps reached
            table.insert(sequence, "..." .. tostring(math.floor(math.log(n, 2)) + 1) .. " more")  -- Estimate remaining steps
            break
        end
        n = collatz_step(n)  -- Perform Collatz step
    end
    collatz_step(n)  -- Final step to 1

    -- Handle 'hide' option
    if hide_sequence then
        return display_steps and ""..(count - 1)..steps or "(sequence is hidden)"
    end

    -- Return formatted sequence
    local result = table.concat(sequence, ", ")
    if display_steps then
        result = result .. " (Total steps: " .. (count - 1) .. ")"
    end
    return result
end

return p