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).

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, 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, 1, 2, 0, 2, 3, 6, 4, 1, 4, 3, 3, 2, 0, 7, 2, 3, 6, 4

Offset: 0

Author

Robert Price, Sep 13 2020

Keywords

• nonn
• base

Examples

			a(42) = 4 because:
1: 42 - 4*2 = 34
2: 34 - 3*4 = 22
3: 22 - 2*2 = 18
4: 18 - 1*8 = 10
5: 10 - 1*0 = 10
		

Links

• Robert Price, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A003001, A070565, A336383.

Programs

Mathematica

Table[Length@  NestWhileList[# - Times @@ IntegerDigits[#] &, n, UnsameQ[##] &,
2] - 2, {n, 0, 85}];(* Robert Price, Sep 13 2020 *)