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Numbers k such that a shortest addition chain for 2*k is shorter than one for k, that is, A003313(2*k) < A003313(k).
3

%I #42 Feb 09 2024 15:33:39

%S 375494703,602641031,619418303,728117339,750793519,750832687,750989359

%N Numbers k such that a shortest addition chain for 2*k is shorter than one for k, that is, A003313(2*k) < A003313(k).

%C Can the shortest addition chain for 2*k be shorter than one for k by more than 1? - _Alexey Slizkov_, Jan 20 2024

%H Neill Michael Clift, <a href="http://dx.doi.org/10.1007/s00607-010-0118-8">Calculating optimal addition chains</a>, Computing 91.3 (2011): 265-284.

%H V. Zhuravlev and P. Samovol, <a href="http://kvant.mccme.ru/pdf/2013/2013-02.pdf">Faster than the fastest, or can one beat the binary algorithm</a>, Kvant 2 (2013), 7-15. (in Russian)

%Y Cf. A003313, A086878, A115016, A256653.

%K nonn,hard,more,nice

%O 1,1

%A _Max Alekseyev_, Oct 22 2013

%E a(1) = 375494703 was found by _Neill M. Clift_ (2011)

%E a(2)-a(7) from _Hugo Pfoertner_, Dec 19 2015