An algorithm which allows digits of a given number to be calculated without requiring the computation of earlier digits. The BBP formula for pi is the best-known such algorithm, but an algorithm also exists for e.
Plouffe (2022) gives a particularly simple digit-extraction algorithm for the decimal digits of 
by defining
 |
(1)
|
Then the 
th
digit to the right of the decimal point of 
for 
is given by
 |
(2)
|
where 
is the integer part and 
is the fractional part.
Similar formulas can be obtained using
 |
(3)
|
and
 |
(4)
|
where 
is an Euler number, which gives a base-9 (or binary)
digit extraction formula (Plouffe 2022). Similar results can be also obtained for
,
,
,
,
,
and 
(Plouffe 2022).
'th Decimal Digit or Binary of 
and 
."