background.js

chrome.tabs.onUpdated.addListener(function(tabId, changeInfo, tab) {
  if (tab.url.match(/\/(\d+)$/)) {
    chrome.pageAction.show(tab.id);
  }
});

chrome.pageAction.onClicked.addListener(function (tab) {
  var nextPageUrl = tab.url.replace(/(\d+)$/, function(match, p1){
      return parseInt(p1) + 1;
  })
  chrome.tabs.update({url: nextPageUrl});
});