DELIMITER //

CREATE PROCEDURE dorepeat(p1 INT, p2 INT)
  BEGIN
    SET @x = p1;
    REPEAT
        UPDATE flats as fl1, (SELECT owned_name FROM flats WHERE id = @x) as fl2 SET fl1.owned_name = fl2.owned_name
        WHERE fl1.id IN (
            SELECT id FROM (
                SELECT id FROM flats
                WHERE owned_name = 'None'
                ORDER BY id ASC
                LIMIT 0, 1
            ) tmp
        ) AND f1.id NOT BETWEEN p1 AND p2 AND fl2.owned_name != 'None';
        UPDATE flats SET owned_name = 'None' WHERE id = @x;
        SET @x = @x + 1;
    UNTIL @x > p2 END REPEAT;
  END
//

CALL dorepeat(122, 157)//