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The encyclopedia of integer sequences
This book presents methods for Computer Investigation of Sequences, a method for hand analysis of sequences, and some of the methods used in this work, as well as suggestions for further study. Expand
On the rapid computation of various polylogarithmic constants
These algorithms can be easily implemented, require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired make it feasible to compute the billionth binary digit of log(2) or π on a modest work station in a few hours run time. Expand
The quest for PI
This article gives a brief history of the analysis and computation of the mathematical constant $\pi = 3.14159 \ldots$, including a number of the formulas that have been used to compute $\pi$ throughExpand
A relative of the Thue-Morse sequence
It is shown that the generating function for c, which encodes the lengths of blocks in the Thue-Morse sequence, is a simple product. Expand
Recognizing Numerical Constants
The advent of inexpensive, high-performance computers and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now existExpand
A Search for a Mathematical Expression for Mass Ratios Using a Large Database
Using a database of 610 millions mathematical constants and expressions a search was conducted in order to find a reasonable expression based on simplicity and length for the mass ratios ofExpand
Exact Formulas for Integer Sequences
A series of formulas are presented that permits the computation of the n'th term using the author customized bootstrap method. That method is a variant of what is described in [GKP]. The { } denotesExpand
Computing the Generating Function of a Series Given Its First Few Terms
This work outlines an approach for the computation of a good candidate for the generating function of a power series for which only the first few coefficients are known by applying the inverse of those transformations to the rational generating function found. Expand
An efficient algorithm for the computation of Bernoulli numbers
This article gives a direct formula for the computation of B (n) using the asymptotic formula
On the computation of the n^th decimal digit of various transcendental numbers
A method for computing the ௧௛ decimal digit of ߨ in ( ଷ ݋() ଷ ) time and with very little memory is presented here. The computation is based on the recently discovered Bailey-Borwein-PlouffeExpand