A035931 - OEIS

%I #14 Dec 30 2019 15:21:19

%S 0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,3,3,3,3,1,2,2,2,

%T 3,3,3,3,3,4,1,2,2,3,3,2,3,4,3,4,1,2,2,3,2,3,2,4,2,3,1,2,3,3,3,2,4,3,

%U 4,3,1,2,3,3,4,4,3,5,3,4,1,2,3,3,3,2,4,3,4,4,1,2,3,4,4,3,3,4,4,3,1

%N Number of steps to reach 0 under "k->max product of two numbers whose concatenation is k".

%H Scott R. Shannon, <a href="/A035931/b035931.txt">Table of n, a(n) for n = 0..10000</a>.

%e a(341)=5 since 341->123->36->18->8->0.

%t f[n_] := If[n<10, 0, With[{d = IntegerDigits[n]}, Table[FromDigits[Take[d, k]]*FromDigits[Drop[d, k]], {k, 1, Length[d]-1}] // Max]];

%t a[n_] := If[n == 0, 0, Length[FixedPointList[f, n]]-2];

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Apr 03 2017 *)

%Y Cf. A035930, A035932, A035933, A035934, A035935.

%K nonn,base,nice

%O 0,12

%A _Erich Friedman_