Find string of decimal digits in Pi
USE test
DROP TABLE IF EXISTS pi;
CREATE TABLE pi
(
    num BLOB
) ENGINE=MyISAM;
INSERT INTO pi VALUES
('3.14159265358...');
SELECT LOCATE('12345',num) FROM pi;

Here is the output
+---------------------+
| locate('12345',num) |
+---------------------+
|               49704 |
+---------------------+
1 row in set (0.03 sec)

I had to go to http://www.piday.org/million/ and scroll/Ctrl-F dozens of times until my web browser found it. Then, I pasted about 60000 characters into that line. Then, I ran the code using MySQL 5.6.21 on my laptop in Windows 8.1.
Have Fun !!!
UPDATE 2015-03-14 15:52 EST
BTW I just discovered this website : 100,000 Digits of Pi.
This displays pi to 100,000 digits instantly. 12345 is also there.
UPDATE 2015-03-14 15:57 EST
I tried the INSTR() function
+--------------------+
| instr(num,'12345') |
+--------------------+
|              49704 |
+--------------------+
1 row in set (0.00 sec)

It works as well !!!