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 A115016 a(n) is the smallest number k that has a shortest addition chain whose length A003313(k) = A003313(n*k), or 0 if this never happens. 10
 1, 191, 171, 30958077, 3277, 2731, 28087 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Using ? to indicate a term whose value is presently unknown, the sequence reads 1, 191, 171, 30958077, 3277, 2731, 28087, ?, 233017, 432541, 953251, 699051, 12905551, 1797559, ?, ?, ?, ?, 7064091, ... This is based on several years work using a variety of algorithms. - Neill M. Clift, May 23 2008 It was conjectured that no shortest addition chains exist such that A003313(m)=A003313(m*2^k) for k>1. This is now known to be false, since a(4) != 0. REFERENCES For a comprehensive list of references see A003313. See also D. E. Knuth, updates to Vol. 2 of TAOCP. LINKS Daniel Bleichenbacher, Efficiency and Security of Cryptosystems based on Number Theory, PhD Thesis, Diss. ETH No. 11404, Zürich 1996; p. 61. Neill Michael Clift, Calculating optimal addition chains, Computing 91.3 (2011): 265-284. EXAMPLE a(3)=171 because 171 and 513=3*171 both have a shortest addition chain of length 10. 171 and 513 is the smallest pair of numbers with the property A003313(k)=A003313(3*k). Examples for the corresponding shortest chains are [1 2 4 5 7 14 19 38 57 114 171] and [1 2 4 8 16 32 64 128 256 512 513]. CROSSREFS Cf. A003313 [l(k)], A086878 [l(k)=l(2*k)], A116459 [l(k)=l(3*k)], A261986 [l(k)=l(4*k)], A116460 [l(k)=l(5*k], A116461 [l(k)=l(6*k)], A116462 [l(k)=l(7*k)], A116463 [l(k)=l(9*k], A117151 [l(k)=l(10*k)]. Sequence in context: A238813 A103494 A104642 * A160784 A139650 A139977 Adjacent sequences:  A115013 A115014 A115015 * A115017 A115018 A115019 KEYWORD nonn,hard,more AUTHOR Hugo Pfoertner, Feb 26 2006 EXTENSIONS a(4) from Neill M. Clift, May 21 2008 STATUS approved

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Last modified July 14 02:55 EDT 2020. Contains 335716 sequences. (Running on oeis4.)