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A009101
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Fixed point when iterating the function f on n, where f(x) = x + product of digits of x.
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0
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0, 102, 102, 102, 102, 10, 102, 102, 102, 102, 10, 102, 102, 102, 102, 20, 102, 102, 102, 60, 20, 110, 102, 110, 102, 50, 102, 140, 60, 110, 30, 70, 102, 50, 70, 50, 102, 170, 102, 102, 40, 140, 50, 80, 60, 140, 70, 110, 80, 150, 50, 170, 102, 202, 102, 80, 170, 110, 170
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Starting at n and iterating f, a(n) is the first number reached that contains digit zero.
Record values of the number of steps to obtain a(n) are 10 for n = 1, 27 for n = 187, 28 for n = 3237326, 32 for n = 3515987, 33 for n = 22572473. It is conjectured that a(n) is obtained in a finite number of steps for every n.
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EXAMPLE
| f(5) = 10, f(10) = 10, hence a(5) = 10; f(19) = 28, f(28) = 44, f(44) = 60, f(60) = 60, hence a(19) = 60.
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CROSSREFS
| Cf. A007954 (product of digits of n).
Sequence in context: A015164 A204749 A144469 * A031962 A135601 A164856
Adjacent sequences: A009098 A009099 A009100 * A009102 A009103 A009104
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KEYWORD
| nonn,base
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| Additional comments from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 12 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 19 2008 at the suggestion of R. J. Mathar
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