Search: id:A003001
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%I A003001 M4687
%S A003001 0,10,25,39,77,679,6788,68889,2677889,26888999,3778888999,
%T A003001 277777788888899
%N A003001 Smallest number of persistence n.
%C A003001 Probably finite.
%C A003001 The persistence of a number (A031346) is the number of times you need 
               to multiply the digits together before reaching a single digit.
%D A003001 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003001 M. Gardner, Fractal Music, Hypercards and More, Freeman, NY, 1991, pp. 
               170, 186.
%D A003001 C. A. Pickover, Wonders of Numbers, "Persistence", Chapter 28, Oxford 
               University Press NY 2001.
%D A003001 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               66.
%H A003001 W. Schneider, <a href="http://www.wschnei.de/digit-related-numbers/persistence.html">
               The Persistence of a Number</a> [Broken link?]
%H A003001 Walter Schneider, <a href="http://www.mathews-archive.com/digit-related-numbers/
               persistence.html">The persistence of a Number</a>, backup of html 
               page.
%H A003001 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/doc/persistence.html">
               The persistence of a number</a>, J. Recreational Math., 6 (1973), 
               97-98.
%H A003001 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MultiplicativePersistence.html">Link to a section of The World of 
               Mathematics.</a>
%H A003001 Wikipedia, <a href="http://en.wikipedia.org/wiki/Persistence_of_a_number">
               Persistence of a number</a>
%e A003001 E.g. 77 -> 49 -> 36 -> 18 -> 8 has persistence 4.
%Y A003001 Cf. A031346 (persistence), A133500 (powertrain), A133048 (powerback).
%Y A003001 Cf. A006050, A007954, A031286, A031347, A033908, A046511, etc.
%Y A003001 Cf. A121105-A121111.
%Y A003001 Sequence in context: A002600 A087473 A014120 this_sequence A038350 A003344 
               A047721
%Y A003001 Adjacent sequences: A002998 A002999 A003000 this_sequence A003002 A003003 
               A003004
%K A003001 nonn,fini,nice,base
%O A003001 0,2
%A A003001 N. J. A. Sloane (njas(AT)research.att.com).

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