0,2

M. Elia and F. Neri, A note on addition chains ..., pp. 166-181 of R. M. Capocelli, ed., Sequences, Springer-Verlag, NY 1990.

D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 458; Vol. 2, 3rd. ed., p. 477.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

See A003313 for a much more extensive list of references and links.

Daniel Bleichenbacher, Efficiency and Security of Cryptosystems based on Number Theory. PhD Thesis, Diss. ETH No. 11404, Zuerich 1996. See p. 60.

Achim Flammenkamp, Shortest addition chains

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).

This is the "smallest inverse" of A003313. Cf. A003065.

Cf. A075530, A115617 [Smallest number for which Knuth's power tree method produces an addition chain of length n].

Sequence in context: A158069 A039726 A115617 this_sequence A057429 A065726 A118985

Adjacent sequences: A003061 A003062 A003063 this_sequence A003065 A003066 A003067

nonn,nice,hard

N. J. A. Sloane (njas(AT)research.att.com) and D. E. Knuth

New terms from Achim Flammenkamp, Math. Diplomarbeit, Univ. Bielefeld, 1991; and from Daniel Bleichenbacher (bleichen(AT)inf.ethz.ch)

a(25)-a(27) from the 3rd. ed. of Knuth vol. 2, sent by David Moulton, Jun 24, 2003.

a(28)-a(30) from the Flammenkamp web site, Feb 01 2005

a(31)=25450463 computed Dec 15 2005 by N. Clift (neillclift(AT)msn.com). - Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 29 2006

a(32)=46444543 computed by N. Clift (neillclift(AT)msn.com), Jun 15 2007

89209343 and 155691199 from N. Clift (neillclift(AT)msn.com), May 21 2008