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An experimental investigation of the normality of irrational algebraic numbers

2013
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Mathematics of Computation
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We investigate the distribution of digits of large prefixes of the expansion of irrational algebraic numbers to different bases. We compute 2·3 18 bits of the binary expansions (corresponding to 2.33·10 8 decimals) of the 39 least Pisot-Vijayaraghavan numbers, the 47 least known Salem numbers, the least 20 square roots of positive integers that are not perfect squares, and 15 randomly generated algebraic irrationals. We employ these to compute the generalized serial statistics (roughly, the

doi:10.1090/s0025-5718-2013-02675-0
fatcat:yssxmzyh3jce3fjmf3ezqeefie