A035931 Number of steps to reach 0 under "k->max product of two numbers whose concatenation is k".

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, 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, 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

Offset: 0

Author

Erich Friedman

Keywords

• nonn
• base
• nice

Examples

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

Links

• Scott R. Shannon, Table of n, a(n) for n = 0..10000.

Crossrefs

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

Programs

Mathematica

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]];
a[n_] := If[n == 0, 0, Length[FixedPointList[f, n]]-2];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 03 2017 *)