How to check any missing number from a series of numbers?

This works on postgres >= 8.4. With some slight modifications to the CTE-syntax it could be made to work for oracle and microsoft, too.

-- EXPLAIN ANALYZE
WITH missing AS (
    WITH RECURSIVE fullhouse AS (
        SELECT MIN(num)+1 as num
        FROM numbers n0
        UNION ALL SELECT 1+ fh0.num AS num
        FROM fullhouse fh0
        WHERE EXISTS (
                SELECT * FROM numbers ex
                WHERE ex.num > fh0.num
                )
        )
        SELECT * FROM fullhouse fh1
        EXCEPT ( SELECT num FROM numbers nx)
        )
SELECT * FROM missing;

A solution without hardcoding the 9:

select min_a - 1 + level
     from ( select min(a) min_a
                 , max(a) max_a
              from test1
          )
  connect by level <= max_a - min_a + 1
    minus
   select a
     from test1

---

Results:

MIN_A-1+LEVEL
-------------
         7003
         7007
         7008
         7009

4 rows selected.

Try this:

SELECT t1.SequenceNumber + 1 AS "From",
       MIN(t2.SequenceNumber) - 1 AS "To"
FROM MyTable t1
JOIN MyTable t2 ON t1.SequenceNumber < t2.SequenceNumber 
GROUP BY t1.SequenceNumber
HAVING t1.SequenceNumber + 1 < MIN(t2.SequenceNumber)

Here is the result for the sequence 7001, 7002, 7004, 7005, 7006, 7010:

From  To
7003  7003
7007  7009

Here's a solution that:

• Relies on Oracle's LAG function
• Does not require knowledge of the complete sequence (but thus doesn't detect if very first or last numbers in sequence were missed)
• Lists the values surrounding the missing lists of numbers
• Lists the missing lists of numbers as contiguous groups (perhaps convenient for reporting)
• Tragically fails for very large lists of missing numbers, due to listagg limitations

SQL:

WITH MentionedValues /*this would just be your actual table, only defined here to provide data for this example */
        AS (SELECT *
              FROM (    SELECT LEVEL + 7000 seqnum
                          FROM DUAL
                    CONNECT BY LEVEL <= 10000)
             WHERE seqnum NOT IN (7003,7007,7008,7009)--omit those four per example
                                       ),
     Ranges /*identifies all ranges between adjacent rows*/
        AS (SELECT seqnum AS seqnum_curr,
                   LAG (seqnum, 1) OVER (ORDER BY seqnum) AS seqnum_prev,
                   seqnum - (LAG (seqnum, 1) OVER (ORDER BY seqnum)) AS diff
              FROM MentionedValues)
SELECT Ranges.*,
       (    SELECT LISTAGG (Ranges.seqnum_prev + LEVEL, ',') WITHIN GROUP (ORDER BY 1)
              FROM DUAL
        CONNECT BY LEVEL < Ranges.diff) "MissingValues" /*count from lower seqnum+1 up to lower_seqnum+(diff-1)*/
  FROM Ranges
 WHERE diff != 1 /*ignore when diff=1 because that means the numers are sequential without skipping any*/
;

Output:

SEQNUM_CURR SEQNUM_PREV DIFF MissingValues
7004        7002        2    "7003" 
7010        7006        4    "7007,7008,7009"