SEQUENCE Storage Engine

The Sequence engine generates virtual tables of number sequences on the fly, useful for generating series of integers without storing data.

This article is about the Sequence storage engine. For details about sequence objects, see Sequences.

A Sequence engine allows the creation of ascending or descending sequences of numbers (positive integers) with a given starting value, ending value and increment.

It creates completely virtual, ephemeral tables automatically when you need them. There is no way to create a Sequence table explicitly. Nor are they ever written to disk or create .frm files. They are read-only, transactional, and support XA.

Installing

The Sequence engine is installed by default, and SHOW ENGINES will list the Sequence storage engine as supported:

SHOW ENGINES\G
...
*************************** 5. row ***************************
      Engine: MyISAM
     Support: YES
     Comment: MyISAM storage engine
Transactions: NO
          XA: NO
  Savepoints: NO
*************************** 6. row ***************************
      Engine: SEQUENCE
     Support: YES
     Comment: Generated tables filled with sequential values
Transactions: YES
          XA: YES
  Savepoints: YES
*************************** 7. row ***************************
      Engine: MRG_MyISAM
     Support: YES
     Comment: Collection of identical MyISAM tables
Transactions: NO
          XA: NO
  Savepoints: NO

...

Usage and Examples

To use a Sequence table, you simply select from it, as in

SELECT * FROM seq_1_to_5;
+-----+
| seq |
+-----+
|   1 |
|   2 |
|   3 |
|   4 |
|   5 |
+-----+

To use a sequence in a statement, you select from the table named by a pattern seq_FROMtoTO or seq_FROMtoTOstepSTEP.

In the case of an odd step, the sequence will commence with the FROM, and end at the final result before TO.

SELECT * FROM seq_1_to_15_step_3;
+-----+
| seq |
+-----+
|   1 |
|   4 |
|   7 |
|  10 |
|  13 |
+-----+

A sequence can go backwards too. In this case the final value will always be the TO value, so that a descending sequence has the same values as an ascending sequence:

SELECT * FROM seq_5_to_1_step_2;
+-----+
| seq |
+-----+
|   5 |
|   3 |
|   1 |
+-----+

SELECT * FROM seq_15_to_1_step_3;
+-----+
| seq |
+-----+
|  13 |
|  10 |
|   7 |
|   4 |
|   1 |
+-----+

SELECT * FROM seq_15_to_2_step_3;
+-----+
| seq |
+-----+
|  14 |
|  11 |
|   8 |
|   5 |
|   2 |
+-----+

This engine is particularly useful with joins and subqueries. For example, this query finds all prime numbers below 50:

SELECT seq FROM seq_2_to_50 s1 WHERE 0 NOT IN
     (SELECT s1.seq % s2.seq FROM seq_2_to_50 s2 WHERE s2.seq <= sqrt(s1.seq));
+-----+
| seq |
+-----+
|   2 |
|   3 |
|   5 |
|   7 |
|  11 |
|  13 |
|  17 |
|  19 |
|  23 |
|  29 |
|  31 |
|  37 |
|  41 |
|  43 |
|  47 |
+-----+

And almost (without 2, the only even prime number) the same result with joins:

SELECT s1.seq FROM seq_2_to_50 s1 JOIN seq_2_to_50 s2 
  WHERE s1.seq > s2.seq AND s1.seq % s2.seq <> 0 
  GROUP BY s1.seq HAVING s1.seq - COUNT(*) = 2;
+-----+
| seq |
+-----+
|   3 |
|   5 |
|   7 |
|  11 |
|  13 |
|  17 |
|  19 |
|  23 |
|  29 |
|  31 |
|  37 |
|  41 |
|  43 |
|  47 |
+-----+

Sequence tables can also be useful in date calculations. For example, to find the day of the week that a particular date has fallen on over a 40 year period (perhaps for birthday planning ahead!):

SELECT DAYNAME('1980-12-05' + INTERVAL (seq) YEAR) day,
    '1980-12-05' + INTERVAL (seq) YEAR DATE FROM seq_0_to_40;
+-----------+------------+
| day       | date       |
+-----------+------------+
| Friday    | 1980-12-05 |
| Saturday  | 1981-12-05 |
| Sunday    | 1982-12-05 |
...
| Friday    | 2014-12-05 |
| Saturday  | 2015-12-05 |
| Monday    | 2016-12-05 |
| Tuesday   | 2017-12-05 |
| Wednesday | 2018-12-05 |
| Thursday  | 2019-12-05 |
| Saturday  | 2020-12-05 |
+-----------+------------+

Although Sequence tables can only directly make use of positive integers, they can indirectly be used to return negative results by making use of the CAST statement:

SELECT CAST(seq AS INT) - 5 x FROM seq_5_to_1;
+----+
| x  |
+----+
|  0 |
| -1 |
| -2 |
| -3 |
| -4 |
+----+

CAST is required to avoid a BIGINT UNSIGNED value is out of range error.

Sequence tables, while virtual, are still tables, so they must be in a database. This means that a default database must be selected (for example, via the USE command) to be able to query a Sequence table. The information_schema database cannot be used as the default for a Sequence table.

Table Name Conflicts

If the SEQUENCE storage engine is installed, it is not possible to create a table with a name which follows the SEQUENCE pattern:

CREATE TABLE seq_1_to_100 (col INT) ENGINE = InnoDB;
ERROR 1050 (42S01): Table 'seq_1_to_100' already exists

However, a SEQUENCE table can be converted to another engine and the new table can be referred in any statement:

ALTER TABLE seq_1_to_100 ENGINE = BLACKHOLE;

SELECT * FROM seq_1_to_100;
Empty set (0.00 sec)

While a SEQUENCE table cannot be dropped, it is possible to drop the converted table. The SEQUENCE table with the same name will still exist:

DROP TABLE seq_1_to_100;

SELECT COUNT(*) FROM seq_1_to_100;
+----------+
| COUNT(*) |
+----------+
|      100 |
+----------+
1 row in set (0.00 sec)

A temporary table with a SEQUENCE-like name can always be created and used:

CREATE TEMPORARY TABLE seq_1_to_100 (col INT) ENGINE = InnoDB;

SELECT * FROM seq_1_to_100;
Empty set (0.00 sec)

Installing

Usage and Examples

Table Name Conflicts

See Also