%I A003064 M0667
%S A003064 1,2,3,5,7,11,19,29,47,71,127,191,379,607,1087,1903,3583,6271,11231,
%T A003064 18287,34303,65131,110591,196591,357887,685951,1176431,2211837,4169527,
%U A003064 7624319,14143037,25450463,46444543,89209343,155691199
%N A003064 Smallest number with addition chain of length n.
%D A003064 M. Elia and F. Neri, A note on addition chains ..., pp. 166-181 of R. 
               M. Capocelli, ed., Sequences, Springer-Verlag, NY 1990.
%D A003064 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, 
               MA, Vol. 2, p. 458; Vol. 2, 3rd. ed., p. 477.
%D A003064 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003064 See A003313 for a much more extensive list of references and links.
%H A003064 Daniel Bleichenbacher, <a href="http://www.bell-labs.com/user/bleichen/
               diss/thesis.html">Efficiency and Security of Cryptosystems based 
               on Number Theory.</a> PhD Thesis, Diss. ETH No. 11404, Zuerich 1996. 
               See p. 60.
%H A003064 Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/addition_chain.html">
               Shortest addition chains</a>
%e A003064 a(7) = 29 because 29 is the smallest number with a shortest addition 
               chain requiring 7 additions. An example of a shortest addition chain 
               for 29 is (1 2 3 4 7 11 18 29).
%Y A003064 This is the "smallest inverse" of A003313. Cf. A003065.
%Y A003064 Cf. A075530, A115617 [Smallest number for which Knuth's power tree method 
               produces an addition chain of length n].
%Y A003064 Sequence in context: A158069 A039726 A115617 this_sequence A057429 A065726 
               A118985
%Y A003064 Adjacent sequences: A003061 A003062 A003063 this_sequence A003065 A003066 
               A003067
%K A003064 nonn,nice,hard
%O A003064 0,2
%A A003064 N. J. A. Sloane (njas(AT)research.att.com) and D. E. Knuth
%E A003064 New terms from Achim Flammenkamp, Math. Diplomarbeit, Univ. Bielefeld, 
               1991; and from Daniel Bleichenbacher (bleichen(AT)inf.ethz.ch)
%E A003064 a(25)-a(27) from the 3rd. ed. of Knuth vol. 2, sent by David Moulton, 
               Jun 24, 2003.
%E A003064 a(28)-a(30) from the Flammenkamp web site, Feb 01 2005
%E A003064 a(31)=25450463 computed Dec 15 2005 by N. Clift (neillclift(AT)msn.com). 
               - Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 29 2006
%E A003064 a(32)=46444543 computed by N. Clift (neillclift(AT)msn.com), Jun 15 2007
%E A003064 89209343 and 155691199 from N. Clift (neillclift(AT)msn.com), May 21 
               2008