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

0,22

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A003001, A070565, A336383.

Sequence in context: A215887 A159451 A378865 * A103159 A063056 A174835

Adjacent sequences: A336679 A336680 A336681 * A336683 A336684 A336685

Keyword

nonn,base

Author

Robert Price, Sep 13 2020

Status

approved