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A336682 a(n) is the number of iterations needed to reach a fixed point starting with n and repeatedly applying f(x) = x - (the product of the digits of x).

%I A336682 #16 Sep 14 2020 20:03:06
%S A336682 0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,2,2,2,2,2,2,2,2,2,0,3,3,3,
%T A336682 3,1,2,2,2,2,0,3,4,4,3,3,3,2,2,2,0,4,5,3,4,1,3,3,2,2,0,2,1,4,1,2,1,3,
%U A336682 1,2,0,2,3,6,4,1,4,3,3,2,0,7,2,3,6,4
%N A336682 a(n) is the number of iterations needed to reach a fixed point starting with n and repeatedly applying f(x) = x - (the product of the digits of x).
%H A336682 Robert Price, <a href="/A336682/b336682.txt">Table of n, a(n) for n = 0..1000</a>
%e A336682 a(42) = 4 because:
%e A336682 1: 42 - 4*2 = 34
%e A336682 2: 34 - 3*4 = 22
%e A336682 3: 22 - 2*2 = 18
%e A336682 4: 18 - 1*8 = 10
%e A336682 5: 10 - 1*0 = 10
%t A336682 Table[Length@  NestWhileList[# - Times @@ IntegerDigits[#] &, n, UnsameQ[##] &,
%t A336682 2] - 2, {n, 0, 85}];(* _Robert Price_, Sep 13 2020 *)
%Y A336682 Cf. A003001, A070565, A336383.
%K A336682 nonn,base
%O A336682 0,22
%A A336682 _Robert Price_, Sep 13 2020