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Stoneham Number


A Stoneham number is a number alpha_(b,c) of the form

 alpha_(b,c)=sum_(k=1)^infty1/(b^(c^k)c^k),

where b,c>1 are relatively prime positive integers. Stoneham (1973) proved that alpha_(b,c) is b-normal whenever c is an odd prime and p is a primitive root of c^2. This result was extended by Bailey and Crandall (2003), who showed that alpha_(b,c) is normal for all positive integers b and c provided only that b and c are relatively prime.


See also

Normal Number

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References

Bailey, D. H. and Crandall, R. E. "Random Generators and Normal Numbers." Exper. Math. 11, 527-546, 2002.Stoneham, R. "On Absolute (j,epsilon)-Normality in the Rational Fractions with Applications to Normal Numbers." Acta Arith. 22, 277-286, 1973.

Referenced on Wolfram|Alpha

Stoneham Number

Cite this as:

Weisstein, Eric W. "Stoneham Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StonehamNumber.html

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