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In this paper we study the $b$-ary expansions of the square roots of thefunction defined by the recurrence $f_b(n)=b f_b(n-1)+n$ with initial value$f(0)=0$ taken at odd positive integers $n$, of which the special case $b=10$is often referred to as the "schizophrenic" or "mock-rational" numbers. Definedby Darling in $2004$ and studied in more detail by Brown in $2009$, theseirrational numbers have the peculiarity of containing long strings of repeatingdigits within their decimal expansion. The main contribution of this paper isthe extension of schizophrenic numbers to all integer bases $b\geq2$ byformally defining the schizophrenic pattern present in the $b$-ary expansion ofthese numbers and the study of the lengths of the non-repeating and repeatingdigit sequences that appear within.

On Schizophrenic Patterns in b-ary Expansions of Some Irrational Numbers