High Quality Content by WIKIPEDIA articles! A spigot algorithm is an algorithm used to compute the value of a mathematical constant such as or e. Unlike recursive algorithms, a spigot algorithm yields digits incrementally without using previously computed digits. The Bailey-Borwein-Plouffe formula for the binary digits of is an example of a spigot algorithm. This example illustrates the working of a spigot algorithm by calculating the binary digits of the natural logarithm of 2 (sequence A068426 in OEIS) using the identity ln(2)=sum_{k=1}^{infty}frac{1}{k2^k}, . To start calculating binary digits from, say, the 8th place we multiply this identity by 27: 2^7ln(2) =2^7sum_{k=1}^{infty}frac{1}{k2^k}, . We then divide the infinite sum into a "head", in which the exponents of 2 are greater than or equal to zero, and a "tail", in which the exponents of 2 are negative: 2^7ln(2) =sum_{k=1}^{7}frac{2^{7-k}}{k}+sum_{k=8}^{infty}frac{1}{k2^{k-7}}, . We are only interested in the fractional part of this value, so we can replace each of the terms in the "head" by frac{2^{7-k} mod k}{k}, .

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