<input type="week">

<label for="week">What week would you like to start?</label>
<input id="week" type="week" name="week" value="2017-W01" />

const weekControl = document.querySelector('input[type="week"]');
weekControl.value = "2017-W45";

<form>
  <label for="week">What week would you like to start?</label>
  <input id="week" type="week" name="week" />
</form>

<form>
  <label for="week">What week would you like to start?</label>
  <input id="week" type="week" name="week" min="2017-W01" max="2017-W52" />
  <span class="validity"></span>
</form>

div {
  margin-bottom: 10px;
  position: relative;
}

input[type="number"] {
  width: 100px;
}

input + span {
  padding-right: 30px;
}

input:invalid + span::after {
  position: absolute;
  content: "✖";
  padding-left: 5px;
}

input:valid + span::after {
  position: absolute;
  content: "✓";
  padding-left: 5px;
}

<form>
  <div>
    <label for="week">What week would you like to start?</label>
    <input
      id="week"
      type="week"
      name="week"
      min="2017-W01"
      max="2017-W52"
      required />
    <span class="validity"></span>
  </div>
  <div>
    <input type="submit" value="Submit form" />
  </div>
</form>

<form>
  <div class="nativeWeekPicker">
    <label for="week">What week would you like to start?</label>
    <input
      id="week"
      type="week"
      name="week"
      min="2017-W01"
      max="2018-W52"
      required />
    <span class="validity"></span>
  </div>
  <p class="fallbackLabel">What week would you like to start?</p>
  <div class="fallbackWeekPicker">
    <div>
      <span>
        <label for="week">Week:</label>
        <select id="fallbackWeek" name="week"></select>
      </span>
      <span>
        <label for="year">Year:</label>
        <select id="year" name="year">
          <option value="2017" selected>2017</option>
          <option value="2018">2018</option>
        </select>
      </span>
    </div>
  </div>
</form>

div {
  margin-bottom: 10px;
  position: relative;
}

input[type="number"] {
  width: 100px;
}

input + span {
  padding-right: 30px;
}

input:invalid + span::after {
  position: absolute;
  content: "✖";
  padding-left: 5px;
}

input:valid + span::after {
  position: absolute;
  content: "✓";
  padding-left: 5px;
}

// Get UI elements
const nativePicker = document.querySelector(".nativeWeekPicker");
const fallbackPicker = document.querySelector(".fallbackWeekPicker");
const fallbackLabel = document.querySelector(".fallbackLabel");

const yearSelect = document.querySelector("#year");
const weekSelect = document.querySelector("#fallbackWeek");

// Hide fallback initially
fallbackPicker.style.display = "none";
fallbackLabel.style.display = "none";

// Test whether a new date input falls back to a text input or not
const test = document.createElement("input");

try {
  test.type = "week";
} catch (e) {
  console.log(e.description);
}

// If it does, run the code inside the if () {} block
if (test.type === "text") {
  // Hide the native picker and show the fallback
  nativePicker.style.display = "none";
  fallbackPicker.style.display = "block";
  fallbackLabel.style.display = "block";

  // populate the weeks dynamically
  populateWeeks();
}

function populateWeeks() {
  // Populate the week select with 52 weeks
  for (let i = 1; i <= 52; i++) {
    const option = document.createElement("option");
    option.textContent = i < 10 ? `0${i}` : i;
    weekSelect.appendChild(option);
  }
}