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
Examples
a(341)=5 since 341->123->36->18->8->0.
Links
- Scott R. Shannon, Table of n, a(n) for n = 0..10000.
Programs
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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 *)