How Persistent am I?
Python 2, 50 39 bytes
-10 thanks to @JonathanAllan
f=lambda x:x>9and-~f(sum(map(int,`x`)))
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Brachylog, 10 bytes
;.{ẹ+}ⁱ⁾Ḋ∧
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Explanation
;.{ }ⁱ⁾ Iterate Output times on the Input…
Ḋ∧ …so that the result is a single digit:
ẹ+ Sum the elements
Prolog (SWI), 91 90 bytes
s(A,B):-A=0,B=0;divmod(A,10,Q,R),s(Q,T),B is T+R.
p(A,B):-A<10,B=0;s(A,S),p(S,T),B is T+1.
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