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A031346
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Multiplicative persistence: number of iterations of "multiply digits" needed to reach a number < 10.
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35
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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)
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OFFSET
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0,26
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REFERENCES
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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
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LINKS
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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
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MAPLE
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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
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PROG
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(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
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CROSSREFS
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Cf. A010888 (additive digital root of n).
Cf. A031286 (additive persistence of n).
Cf. A031347 (multiplicative digital root of n).
Sequence in context: A102675 A177849 A143544 * A087472 A172069 A054348
Adjacent sequences: A031343 A031344 A031345 * A031347 A031348 A031349
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KEYWORD
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nonn,easy,base
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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