A105195 -id:A105195 - cp's OEIS frontend

A138161 Erroneous version of A105195.

1, 2, 2, 3, 4, 4, 4, 5, 5

Offset: 2

dead

Daniel Bleichenbacher, Efficiency and Security of Cryptosystems based on Number Theory. PhD Thesis, Diss. ETH No. 11404, Zuerich 1996. See p. 64.

A105096 Length of shortest Lucas chain for n.

0, 1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 6, 5, 6, 5, 6, 6, 7, 5, 6, 6, 6, 6, 7, 6, 7, 5, 7, 7, 7, 6, 8, 7, 7, 6, 8, 7, 8, 7, 7, 8, 8, 6, 8, 7, 8, 7, 9, 7, 8, 7, 8, 8, 9, 7, 9, 8, 8, 6, 8, 8, 9, 8, 9, 8, 9, 7, 9, 9, 8, 8, 9, 8, 9, 7, 8, 9, 10, 8, 9, 9, 9

Offset: 1

N. J. A. Sloane, May 23 2008

nonn

Lucas chains are addition chains with additional requirements on the presence of differences between members of the chain. Therefore a(n) >= A003313(n) and A104892(n) <= A003064(n). Shortest simple Lucas chains are constrained even further (forbid duplication between adjacent members). Therefore a(n) <= A105195(n). - R. J. Mathar, May 24 2008

Jinyuan Wang, Table of n, a(n) for n = 1..10000
Daniel Bleichenbacher, Efficiency and Security of Cryptosystems based on Number Theory. PhD Thesis, Diss. ETH No. 11404, Zuerich 1996. See p. 64.
Neill Clift, Lucas/Differential Addition Chains.
Wikipedia, Lucas chain.
Index to sequences related to the complexity of n

Cf. A003313, A104892, A105195, A266082.

Offset changed to 1 and more terms from Jinyuan Wang, Apr 18 2025

A104892 Smallest number whose shortest Lucas chain is of length n.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 23, 37, 53, 83, 127, 197, 331, 461, 739, 1123, 1801, 2903, 4463, 6947, 10973, 17539, 26627, 43103, 67079, 109639, 160649, 271829, 432199, 665789, 1080491, 1666943, 2668909, 4182169, 6786257, 10612027, 17010151, 26901547, 42105257, 67208321, 105414851, 169631897, 265359847, 423344501, 672662981, 1065233261, 1653387299, 2680042177, 4243717559, 6698246557

Offset: 1

N. J. A. Sloane, May 23 2008

nonn

Daniel Bleichenbacher, Efficiency and Security of Cryptosystems based on Number Theory, PhD Thesis, Diss. ETH No. 11404, Zürich 1996. See p. 69.
Neill Clift, Lucas/Differential Addition Chains.
Wikipedia, Lucas chain.
Index to sequences related to the complexity of n

Cf. A105096, A105195, A003313.

a(30) onwards from Neill M. Clift, Oct 19 2024

cp's OEIS Frontend

A138161 Erroneous version of A105195.

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A105096 Length of shortest Lucas chain for n.

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A104892 Smallest number whose shortest Lucas chain is of length n.

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