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

0,12

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A098378 A160093 A259143 * A330634 A254524 A374097

Adjacent sequences: A035928 A035929 A035930 * A035932 A035933 A035934

Keyword

nonn,base,nice

Author

Erich Friedman

Status

approved