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A035931 Number of steps to reach 0 under "k->max product of two numbers whose concatenation is k". 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Table of n, a(n) for n=0..100.

EXAMPLE

a(123)=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-Fran├žois Alcover, Apr 03 2017 *)

CROSSREFS

Cf. A035930-A035935.

Sequence in context: A098378 A160093 A259143 * A254524 A140438 A132211

Adjacent sequences:  A035928 A035929 A035930 * A035932 A035933 A035934

KEYWORD

nonn,base,nice

AUTHOR

Erich Friedman

STATUS

approved

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Last modified February 18 09:38 EST 2019. Contains 320249 sequences. (Running on oeis4.)