A spigot algorithm for the digits of \(\pi\). (English) Zbl 0853.11102

Rabinowitz, Stanley; Wagon, Stan

Am. Math. Mon. 102, No. 3, 195-203 (1995).

A spigot algorithm produces in succession the digits of a given number: it uses only simple operations on relatively small integers, and so is easily implemented on a home computer.
Such an algorithm for \(e\) was devised by A. H. J. Sale [Comput. J. 11, 229-230 (1968; Zbl 0155.48703)]: the authors give one for \(\pi\) based on the fact that, with respect to the mixed-radix base \((1/3, 2/5, \dots, m/(2m+ 1), \dots)\), \(\pi\) is \((2; 2, 2,\dots)\). A better, but less simple, base has been obtained by R. W. Gosper [Memo No. 304, M.I.T. Artificial Intelligence Laboratory, Cambridge, Mass (1970)].

Reviewer: H.J.Godwin (Egham)

MSC:

11Y60	Evaluation of number-theoretic constants
11A63	Radix representation; digital problems
11Y16	Number-theoretic algorithms; complexity
11A25	Arithmetic functions; related numbers; inversion formulas

Keywords:

spigot algorithm for the digits of \(\pi\); mixed-radix base

Citations:

Zbl 0155.48703