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A335808 Nonzero multiplicative persistence in base 10: number of iterations of "multiply nonzero digits in base 10" needed to reach a number < 10. 1
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,26

COMMENTS

Coincides with A031346 up to n=204.

Differs from A087472 first at n=110. - R. J. Mathar, Aug 10 2020

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E16, pages 262-263.

LINKS

Lucas Colucci, Table of n, a(n) for n = 0..9999

Gabriel Bonuccelli, Lucas Colucci, and Edson de Faria, On the Erdős-Sloane and Shifted Sloane Persistence, arXiv:2009.01114 [math.NT], 2020.

MAPLE

A335808 := proc(n)

    option remember;

    if n < 10 then

        0 ;

    elif n < 20 then

        1 ;

    else

        A051801(n) ;

        1+procname(%) ;

    end if;

end proc: # R. J. Mathar, Aug 10 2020

MATHEMATICA

Array[-1 + Length[NestWhileList[Times @@ DeleteCases[IntegerDigits[#], _?(# == 0 &)] &, #, # >= 10 &]] &, 105, 0] (* Michael De Vlieger, Jun 24 2020 *)

PROG

(PARI) a(n) = for (k=0, oo, if (n<10, return (k), n=vecprod(select(sign, digits(n))))) \\ Rémy Sigrist, Jul 18 2020

CROSSREFS

Cf. A031346, A051801.

Sequence in context: A177849 A143544 A031346 * A087472 A172069 A054348

Adjacent sequences:  A335805 A335806 A335807 * A335809 A335810 A335811

KEYWORD

nonn,base,easy

AUTHOR

Lucas Colucci, Jun 24 2020

STATUS

approved

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Last modified May 11 07:23 EDT 2021. Contains 343784 sequences. (Running on oeis4.)