Police said that Anthony, 67, was last seen at about 8.20pm on May 26 in the town.
A police spokesperson added: “Anthony is 5'7" with a grey beard and long grey shoulder-length hair.
"He was last seen wearing a green jacket, jeans, and green trainers.
"Anyone who sees him or knows his whereabouts is asked to report it to Sussex Police by calling 101 and quote serial 773 of 27/05.”