Stoneham Number

A Stoneham number is a number  of the form

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

REFERENCES:

Bailey, D. H. and Crandall, R. E. "Random Generators and Normal Numbers." Exper. Math. 11, 527-546, 2002.

Stoneham, R. "On Absolute -Normality in the Rational Fractions with Applications to Normal Numbers." Acta Arith. 22, 277-286, 1973.