A real number
is said to be -dense
iff, in the base- expansion of , every possible finite string of consecutive digits appears.
If is -normal, then is also -dense. If, for some ,
is -dense, then is irrational. Finally, is -dense
iff the sequence is dense (Bailey and Crandall 2001, 2003).
Bailey, D. H. and Crandall, R. E. "On the Random Character of Fundamental Constant Expansions." Exper. Math.10,
175-190, 2001.Bailey, D. H. and Crandall, R. E. "Random
Generators and Normal Numbers." Exper. Math.11, 527-546, 2002.