

A003065


Number of integers with a shortest addition chain of length n.
(Formerly M0707)


7



1, 1, 2, 3, 5, 9, 15, 26, 44, 78, 136, 246, 432, 772, 1382, 2481, 4490, 8170, 14866, 27128, 49544, 90371, 165432, 303475, 558275, 1028508, 1896704, 3501029, 6465774, 11947258, 22087489, 40886910, 75763102, 140588339
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OFFSET

0,3


REFERENCES

M. Elia and F. Neri, A note on addition chains ..., pp. 166181 of R. M. Capocelli, ed., Sequences, SpringerVerlag, NY 1990.
D. E. Knuth, The Art of Computer Programming. AddisonWesley, Reading, MA, Vol. 2, p. 459.
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.


LINKS

R. J. Mathar, Table of n, a(n) for n = 0..38
Daniel Bleichenbacher, Efficiency and Security of Cryptosystems based on Number Theory. PhD Thesis, Diss. ETH No. 11404, Zuerich 1996. See p. 61.
Achim Flammenkamp, Shortest addition chains
Index to sequences related to the complexity of n


EXAMPLE

a(6) = 15 because 15 numbers have shortest addition chains involving 6 additions. These numbers are 19,21,22,23,25,26,27,28,30,33,34,36,40,48,64.


CROSSREFS

Cf. A003064, A003313.
Cf. A114623 [Number of integers for which Knuth's power tree method produces an addition chain of length n].
Sequence in context: A286887 A018157 A228644 * A239909 A185648 A228645
Adjacent sequences: A003062 A003063 A003064 * A003066 A003067 A003068


KEYWORD

nonn,nice,hard


AUTHOR

N. J. A. Sloane, Don Knuth


EXTENSIONS

Updated through a(28) from the Flammenkamp web site Feb 01 2005
a(28) corrected from 6465773 to 6465774, based on information received from N. Clift (neillclift(AT)msn.com).  Hugo Pfoertner, Jan 29 2006
a(29)=11947258 and a(30)=22087489 computed by N. Clift (neillclift(AT)msn.com), Jun 15 2007
40886910, 75763102, 140588339 from N. Clift (neillclift(AT)msn.com), May 21 2008
bfile up to a(38) extracted from Flammenkamp's web site. R. J. Mathar, May 14 2013


STATUS

approved



