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A014553
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Maximal multiplicative persistence (or length) of any n-digit number.
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5
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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
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1,2
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COMMENTS
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The "persistence" or "length" of an N-digit decimal number is the number of times one must iteratively form the product of its digits until one obtains a one-digit 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
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REFERENCES
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Gottlieb, A. J. Problems 28-29 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.
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LINKS
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EXAMPLE
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168889 is not in A003001 because a(6) = a(5) = 7.
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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