Well, because of my understanding, it seems like the OP wants to redirect the user to the URL of the search results. Using the GoogleAPI would be the first choice and achieve something similar, I would do this:
<?php
$query = "firefox";
$apiUrl = "http://ajax.googleapis.com/ajax/services/search/web?v=1.0&q=".urlencode($query);
$ch = curl_init();
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
curl_setopt($ch, CURLOPT_URL, $apiUrl);
$content = curl_exec($ch);
$content = json_decode($content);
$luckyUrl = $content->responseData->results[0]->unescapedUrl;
header("Location: ".$luckyUrl);
?>
The code above works like "I'm in luck" ....