

A014553


Maximal multiplicative persistence (or length) of any ndigit number.


4



1, 4, 5, 6, 7, 7, 8, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
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OFFSET

1,2


COMMENTS

The "persistence" or "length" of an Ndigit decimal number is the number of times one must iteratively form the product of its digits until one obtains a onedigit product (For another definition see A003001.)
For all other n<2530, a[n]=11 because sequence is nondecreasing and a number with multiplicative persistence 12 must have more than 2530 digits.  Sascha Kurz, Mar 24 2002


REFERENCES

Gottlieb, A. J. Problems 2829 in ``Bridge, Group Theory and a Jigsaw Puzzle.'' Techn. Rev. 72, unpaginated, Dec. 1969.
Gottlieb, A. J. Problem 29 in ``Integral Solutions, Ladders and Pentagons.'' Techn. Rev. 72, unpaginated, Apr. 1970.


LINKS

Table of n, a(n) for n=1..72.
Beeler, M., Gosper, R. W. and Schroeppel, R., HAKMEM, ITEM 56
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 9798.
Eric Weisstein's World of Mathematics, Multiplicative Persistence.


EXAMPLE

168889 is not in A003001 because a(6) = a(5) = 7


CROSSREFS

Cf. A003001, A031346, A035927.
Sequence in context: A114546 A067471 A102691 * A227422 A121855 A239440
Adjacent sequences: A014550 A014551 A014552 * A014554 A014555 A014556


KEYWORD

nonn,easy,base


AUTHOR

Eric W. Weisstein


EXTENSIONS

Corrected by N. J. A. Sloane 11/95.
More terms from John W. Layman, Mar 19 2002


STATUS

approved



