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A031346 Multiplicative persistence: number of iterations of "multiply digits" needed to reach a number < 10. 36
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

REFERENCES

M. Gardner, Fractal Music, Hypercards and More Mathematical Recreations from Scientific American, Persistence of Numbers, pp. 120-1; 186-7, W. H. Freeman NY 1992

LINKS

T. D. Noe, Table of n, a(n) for n=0..10000

M. R. Diamond, Multiplicative persistence base 10: some new null results.

N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.

Eric Weisstein's World of Mathematics, Multiplicative Persistence

MAPLE

A007954 := proc(n) return mul(d, d=convert(n, base, 10)): end: A031346 := proc(n) local k, m: k:=0:m:=n: while(length(m)>1)do m:=A007954(m):k:=k+1: od: return k: end: seq(A031346(n), n=0..100); # Nathaniel Johnston, May 04 2011

PROG

(Python)

from operator import mul

from functools import reduce

def A031346(n):

....mp = 0

....while (n > 9):

........n = reduce(mul, (int(d) for d in str(n)))

........mp += 1

....return mp

# Chai Wah Wu, Aug 23 2014

CROSSREFS

Cf. A010888 (additive digital root of n).

Cf. A031286 (additive persistence of n).

Cf. A031347 (multiplicative digital root of n).

Cf. A263131 (ordinal transform of a).

Sequence in context: A102675 A177849 A143544 * A087472 A172069 A054348

Adjacent sequences:  A031343 A031344 A031345 * A031347 A031348 A031349

KEYWORD

nonn,easy,base

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified February 9 02:39 EST 2016. Contains 268100 sequences.