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%I #12 Aug 27 2022 02:49:20
%S 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
%N Length of shortest simple Lucas chain for n.
%C Lucas chains are addition chains with additional requirements on the presence of differences between members of the chain.
%C (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).
%C (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
%H 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. 64.
%H <a href="/index/Com#complexity">Index to sequences related to the complexity of n</a>
%e 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.
%e 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
%Y Cf. A104892, A105096, A003313.
%K nonn
%O 2,2
%A _N. J. A. Sloane_, May 23 2008
%E a(11)-a(36) added by _R. J. Mathar_, May 24 2008