Change amount of posts displayed on search results page

I’d like to have only one post displayed on the main page and have multiple posts displayed on the search results page. The built-in Settings->Read->show posts per page variable seems to be shared by these two pages.

When I change that variable it changes the amount of results shown on the search page but it also changes the amount of posts shown on the main page. Is there a way to modify one but not the other?