

A105195


Length of shortest simple Lucas chain for n.


3



1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 8, 8, 7, 8, 8
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OFFSET

2,2


COMMENTS

Lucas chains are addition chains with additional requirements on the presence of differences between members of the chain.
(i) a(4) is given as 2 in Table 5.1 of the reference, which probably is a typographical error since the length of the example obviously is the same as for a(5).
(ii) Other authors call a(n)+1 the length of the chain, i.e., they include the first 1 of the chain in the count.  R. J. Mathar, May 24 2008


LINKS

Table of n, a(n) for n=2..36.
Daniel Bleichenbacher, Efficiency and Security of Cryptosystems based on Number Theory. PhD Thesis, Diss. ETH No. 11404, Zuerich 1996. See p. 64.
Index to sequences related to the complexity of n


EXAMPLE

Chain for n=11: (0,1,2,3,4,7,11), length 5. Chain for n=12: (0,1,2,3,5,7,12), length 5.
Chain for n=13: (0,1,2,3,5,8,13), length 5. Chain for n=14: (0,1,2,3,4,5,9,14), length 6.  R. J. Mathar, May 24 2008


CROSSREFS

Cf. A104892, A105096, A003313.
Sequence in context: A213711 A072649 A266082 * A257569 A039836 A083398
Adjacent sequences: A105192 A105193 A105194 * A105196 A105197 A105198


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, May 23 2008


EXTENSIONS

a(11)a(36) added by R. J. Mathar, May 24 2008


STATUS

approved



