WITH DATA AS (SELECT num,MAX(num) OVER() m
                FROM (SELECT CASE
                                WHEN SUM (num) OVER (ORDER BY num) > 1000
                                   THEN   num
                                        - (  SUM (num) OVER (ORDER BY num)
                                           - 1000
                                          )
                                ELSE num
                             END AS num
                        FROM (SELECT POWER (2, LEVEL - 1) AS num
                               FROM DUAL
                              CONNECT BY POWER (2, LEVEL - 1) <= 1000
                              )
                      )
               )
,TO_CHECK AS (SELECT ROWNUM n FROM DUAL CONNECT BY ROWNUM <=1000)
SELECT n
  FROM (
SELECT n,num
  FROM TO_CHECK, DATA
 WHERE (CASE WHEN n>m THEN n-m ELSE n END)>num-1 AND BITAND((CASE WHEN n>m THEN n-m ELSE n END),num)>0 AND num < m
        OR (n>m AND num=m)
 )
GROUP BY n HAVING SUM(num) != n

Or:

WITH DATA AS (SELECT num,MAX(num) OVER() m
                FROM (SELECT CASE
                                WHEN SUM (num) OVER (ORDER BY num) > 1000
                                   THEN   num
                                        - (  SUM (num) OVER (ORDER BY num)
                                           - 1000
                                          )
                                ELSE num
                             END AS num
                        FROM (SELECT POWER (2, LEVEL - 1) AS num
                               FROM DUAL
                              CONNECT BY POWER (2, LEVEL - 1) < = 1000
                              )
                      )
               )
,TO_CHECK AS (SELECT ROWNUM n FROM DUAL CONNECT BY ROWNUM  <=1000)
SELECT num FROM DATA
WHERE NOT EXISTS (
SELECT n
  FROM (
SELECT n,num
  FROM TO_CHECK, DATA
 WHERE (CASE WHEN n>m THEN n-m ELSE n END)>num-1 AND BITAND((CASE WHEN n>m THEN n-m ELSE n END),num)>0 AND num < m
        OR (n>m AND num=m)
 )
GROUP BY n HAVING SUM(num) != n
)
;