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Search: id:A014553
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| A014553 |
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Maximal multiplicative persistence (or length) of any n-digit number. |
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+0
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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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 non-decreasing and a number with multiplicative persistence 12 must have more than 2530 digits. - Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), 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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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), 97-98.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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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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Cf. A003001, A031346, A035927.
Sequence in context: A114546 A067471 A102691 this_sequence A121855 A090925 A143836
Adjacent sequences: A014550 A014551 A014552 this_sequence A014554 A014555 A014556
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KEYWORD
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nonn,easy,base
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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Corrected by N. J. A. Sloane (njas(AT)research.att.com) 11/95.
More terms from John W. Layman (layman(AT)math.vt.edu), Mar 19 2002
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