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 bestknown such algorithm, but an algorithm also exists for e.
Plouffe (2022) gives a particularly simple digitextraction 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 base9 (or binary) digit extraction formula (Plouffe 2022). Similar results can be also obtained for , , , , , and (Plouffe 2022).