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A105195 Length of shortest simple Lucas chain for n.

%I A105195 #16 Apr 19 2025 04:34:22
%S A105195 0,1,2,3,3,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,6,7,7,7,7,7,7,8,7,7,7,8,8,7,
%T A105195 8,8,8,8,8,8,8,8,8,8,8,8,8,9,8,8,9,9,9,9,8,9,9,9,9,9,9,9,9,9,9,9,9,9,
%U A105195 9,9,9,10,9,9,9,9,10,10,9,9,9,10,10,10,10
%N A105195 Length of shortest simple Lucas chain for n.
%C A105195 Lucas chains are addition chains with additional requirements on the presence of differences between members of the chain.
%C A105195 (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 A105195 (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 A105195 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 A105195 Neill Clift, <a href="http://additionchains.com/Lucas.html">Lucas/Differential Addition Chains</a>.
%H A105195 <a href="/index/Com#complexity">Index to sequences related to the complexity of n</a>
%e A105195 Chain for n=11: (1,2,3,4,7,11), length 5. Chain for n=12: (1,2,3,5,7,12), length 5.
%e A105195 Chain for n=13: (1,2,3,5,8,13), length 5. Chain for n=14: (1,2,3,4,5,9,14), length 6. - _R. J. Mathar_, May 24 2008
%Y A105195 Cf. A003313, A104892, A105096, A266082.
%K A105195 nonn
%O A105195 1,3
%A A105195 _N. J. A. Sloane_, May 23 2008
%E A105195 a(11)-a(36) added by _R. J. Mathar_, May 24 2008
%E A105195 a(1) prepended by and a(37)-a(85) from _Jinyuan Wang_, Apr 18 2025