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Search: id:A003001
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| A003001 |
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Smallest number of persistence n.
(Formerly M4687)
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+0
42
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| 0, 10, 25, 39, 77, 679, 6788, 68889, 2677889, 26888999, 3778888999, 277777788888899
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Probably finite.
The persistence of a number (A031346) is the number of times you need to multiply the digits together before reaching a single digit.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Gardner, Fractal Music, Hypercards and More, Freeman, NY, 1991, pp. 170, 186.
C. A. Pickover, Wonders of Numbers, "Persistence", Chapter 28, Oxford University Press NY 2001.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 66.
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LINKS
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W. Schneider, The Persistence of a Number [Broken link?]
Walter Schneider, The persistence of a Number, backup of html page.
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.
Wikipedia, Persistence of a number
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EXAMPLE
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E.g. 77 -> 49 -> 36 -> 18 -> 8 has persistence 4.
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CROSSREFS
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Cf. A031346 (persistence), A133500 (powertrain), A133048 (powerback).
Cf. A006050, A007954, A031286, A031347, A033908, A046511, etc.
Cf. A121105-A121111.
Sequence in context: A002600 A087473 A014120 this_sequence A038350 A003344 A047721
Adjacent sequences: A002998 A002999 A003000 this_sequence A003002 A003003 A003004
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KEYWORD
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nonn,fini,nice,base
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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