A valuable early painting by Georgia O'Keeffe will be auctioned this month after art experts solved the mystery of where it has been since 1924. For most of the time, it was in a private collection on Cape Cod. The artist's "Alligator Pear in White Dish," painted in 1921, is expected to sell for $100,000 to $150,000 on Jan. 29 at Skinner Inc. in Boston. The sellers are descendants of Katrina Grullemans of Chatham, who bought the 9-by-12-inch O'Keeffe painting for $500 in 1954 at the Mayo Hill Galleries in Wellfleet.