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%I #25 Sep 03 2020 12:18:56
%S 0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,1,1,1,1,
%T 2,2,2,2,2,3,1,1,1,2,2,2,2,3,2,3,1,1,2,2,2,3,2,3,2,3,1,1,2,2,2,2,3,2,
%U 3,3,1,1,2,2,3,3,2,4,3,3,1,1,2,2,2,2,3,3,3,3,1,1,2,3,3,3,3,3,3,2
%N Nonzero multiplicative persistence in base 10: number of iterations of "multiply nonzero digits in base 10" needed to reach a number < 10.
%C Coincides with A031346 up to n=204.
%C Differs from A087472 first at n=110. - _R. J. Mathar_, Aug 10 2020
%D R. K. Guy, Unsolved Problems in Number Theory, E16, pages 262-263.
%H Lucas Colucci, <a href="/A335808/b335808.txt">Table of n, a(n) for n = 0..9999</a>
%H Gabriel Bonuccelli, Lucas Colucci, and Edson de Faria, <a href="https://arxiv.org/abs/2009.01114">On the Erdős-Sloane and Shifted Sloane Persistence</a>, arXiv:2009.01114 [math.NT], 2020.
%p A335808 := proc(n)
%p option remember;
%p if n < 10 then
%p 0 ;
%p elif n < 20 then
%p 1 ;
%p else
%p A051801(n) ;
%p 1+procname(%) ;
%p end if;
%p end proc: # _R. J. Mathar_, Aug 10 2020
%t Array[-1 + Length[NestWhileList[Times @@ DeleteCases[IntegerDigits[#], _?(# == 0 &)] &, #, # >= 10 &]] &, 105, 0] (* _Michael De Vlieger_, Jun 24 2020 *)
%o (PARI) a(n) = for (k=0, oo, if (n<10, return (k), n=vecprod(select(sign, digits(n))))) \\ _Rémy Sigrist_, Jul 18 2020
%Y Cf. A031346, A051801.
%K nonn,base,easy
%O 0,26
%A _Lucas Colucci_, Jun 24 2020
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