Curious as to how certain irrationals called "schizophrenic numbers" can present long (theoretically infinitely long) repeating (i.e. clearly non random) patterns


"For any positive integer n let
f(n) denote the integer given by the recurrence

f(n) = 10 f(n-1) + n

with the initial value f(0) = 0. Thus we have f(1)=1, f(2)=12,
f(3)=123, and so on. The square roots of f(n) for odd integers
n give a persistent pattern, appearng to be rational for periods,
and then disintegrating into irrationality. This is illustrated
by the first 500 digits of sqrt[f(49)] "

what the fuck