How can we find gaps in sequential numbering in MySQL?

Solution #1

SELECT (t1.id + 1) as gap_starts_at,
       (SELECT MIN(t3.id) -1 FROM arrc_vouchers t3 WHERE t3.id > t1.id) as gap_ends_at
FROM arrc_vouchers t1
WHERE NOT EXISTS (SELECT t2.id FROM arrc_vouchers t2 WHERE t2.id = t1.id + 1)
HAVING gap_ends_at IS NOT NULL
gap_starts_at - first id in current gap
gap_ends_at - last id in current gap

Reference: https://stackoverflow.com/a/6057665/6875460

Solution #2

## More efficient!

SELECT
  CONCAT(z.expected, IF(z.got-1>z.expected, CONCAT(' thru ',z.got-1), '')) AS missing
FROM (
  SELECT
    @rownum:=@rownum+1 AS expected,
    IF(@rownum=YourCol, 0, @rownum:=YourCol) AS got
  FROM
    (SELECT @rownum:=0) AS a
    JOIN YourTable
    ORDER BY YourCol
  ) AS z
WHERE z.got!=0;

Reference: https://stackoverflow.com/a/29736658/6875460