Vertical gradient formula

I want to write a C program that produces 1000x1000 .ppm file, showing a vertical gradient from black(left) to white (right). Now, if the picture would be 256x256 it would be easy:

P3
256 256
255
0 0 0 1 1 1 2 2 2 .... 255 255 255
0 0 0 1 1 1 2 2 2 .... 255 255 255
.
.
.
0 0 0 1 1 1 2 2 2 .... 255 255 255

Thing is, since it must be 1000x1000 (exceeding 255), I'm not sure what formula I should follow to get a perfect gradient. Any ideas?

You can scale the pixel's color index by the total desired width to generate a decimal between 0 and 1 that represents its normalized position within the line. Then multiply by 256 to scale it to the color range. This gives:

int color = (float)offset / width * 256;

Runnable proof of concept:

const makeGradient = (gradEl, width=500, height=500) => {
  let html = "";
  
  for (let offset = 0; offset < width; offset++) {
    const color = offset / width * 256; // JS does float division
    html += `
      <div style="
        background-color: rgb(${color}, ${color}, ${color});
        width: 1px; height: ${height}px;
      "></div>
    `;
  }
  
  gradEl.innerHTML = html;
};

const gradEl = document.querySelector("#gradient");
makeGradient(gradEl);
document.querySelector("input")
  .addEventListener("keyup", e => {
    makeGradient(gradEl, +e.target.value || null);
  });

body {
  background: blue;
}

#gradient {
  display: flex;
}

<input value="500" type="number" min="0" max="2000">
<div id="gradient"></div>