A335808 Nonzero multiplicative persistence in base 10: number of iterations of "multiply nonzero digits in base 10" needed to reach a number < 10.

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

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