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A245760 Maximal multiplicative persistence of n in any base. 2
0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

It has been conjectured that there is a maximum multiplicative persistence in a given base, but it is not known if this sequence is bounded.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

EXAMPLE

a(23)=3 since the persistence of 23 in base 6 is 3 (23 in base 6 is 35 / 3x5=15 / 15 in base 6 is 23 / 2x3=6 / 6 in base 6 is 10 / 1x0=0 which is a single digit). In any other base the persistence of 23 is 3 or less, therefore a(23)=3.

a(12)=1 since 12 does not have a multiplicative persistence greater than 1 in any base.

MAPLE

persistence:= proc(n, b) local i, m;

  m:= n;

  for i from 1 do

       m:= convert(convert(m, base, b), `*`);

     if m < b then return i fi

  od:

end proc:

A:= n -> max(seq(persistence(n, b), b=2..n-1)):

0, 1, seq(A(n), n=3..100); # Robert Israel, Jul 31 2014

PROG

persistence[n_, b_] := Module[{i, m}, m = n; For[i = 1, True, i++, m = Times @@ IntegerDigits[m, b]; If[m < b, Return [i]]]];

A[n_] := Max[Table[persistence[n, b], {b, 2, n-1}]];

Join[{0, 1}, Table[A[n], {n, 3, 100}]] (* Jean-Fran├žois Alcover, Apr 30 2019, after Robert Israel *)

CROSSREFS

Cf. A003001, A031346, A064867, A064868, A046510.

Sequence in context: A264998 A118916 A107800 * A085761 A102382 A024890

Adjacent sequences:  A245757 A245758 A245759 * A245761 A245762 A245763

KEYWORD

nonn

AUTHOR

Sergio Pimentel, Jul 31 2014

STATUS

approved

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Last modified November 14 07:13 EST 2019. Contains 329111 sequences. (Running on oeis4.)