A simply strongly normal number to base 
is a real number 
for which the number 
of occurrences of the digit 
among the first 
digits in the base-
expansion satisfies
 |  |  |
(1)
|
 |  |  |
(2)
|
for every base-
digit 
(Belshaw and Borwein 2013). Thus its single-digit frequencies
have the fluctuations specified by the law
of the iterated logarithm. Every simply strongly normal number is simply normal.
