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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.)