I agree with both broll and Praneeth that the next three numbers are 20, 18, and 5.

The standard QWERTY keyboard's top row of letters, right to left, (i.e., reverse order) are:  
 P   O   I   U   Y   T   R   E   W   Q
Assigning these letters their positional value in the alphabet gives:
16  15   9  21  25  20  18   5  23  17
As can be seen the next three numbers (and letters) in the sequence are:  20 (T), 18 (R), and 5 (E).

broll's comment that the sequence may continue with 26, 1 or 23, 17 is a reference that not all keyboards are QWERTY. The AZERTY keyboard, primarily used by some French-European speakers, has the same (reverse) sequence of eight letters on the top row of letters.  If one was to base the sequence on the  Sholes-Glidden "Type Writer" offered to Remington in 1873, the next three numbers (and letters) of the sequence would be:
20 (T), 5 (E), 23 (W). This ignores the non-letter, the period (.), to which the R was shortly relocated to replace its position.

Posted by Dej Mar on 2010-06-23 06:27:00