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A105195
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Length of shortest simple Lucas chain for n.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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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 typographic 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, ie, they include the first 1 of the chain in the count. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 24 2008
a(11)-a(36) added by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 24 2008
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LINKS
| Daniel Bleichenbacher, Efficiency and Security of Cryptosystems based on Number Theory. PhD Thesis, Diss. ETH No. 11404, Zuerich 1996. See p. 64.
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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 (mathar(AT)strw.leidenuniv.nl), May 24 2008
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CROSSREFS
| Cf. A104892, A105096, A003313.
Sequence in context: A129382 A163515 A072649 * A039836 A083398 A061420
Adjacent sequences: A105192 A105193 A105194 * A105196 A105197 A105198
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 23 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 24 2008
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