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BBP's formula for pi
With the formula of Bailey, Borwein and Plouffe you can calculate any binary or hexadecimal position of the number pi
There is no such similar formula for base-10 digits of π.
Details
Using the formula you can calculate any position, without first calculating the previous positions.
In base-2 writing is π = 11,0010 0100 0011 1111… and in base-16 is π = 3,243F 6A88 85A3 08D3…