cp's OEIS Frontend

A048200 Minimal length pair-exchange / set-rotate sequence to reverse n distinct ordered elements.

%I A048200 #61 Jun 25 2025 23:19:19
%S A048200 0,1,2,4,10,15,23,32,42,55,67,84,98,119
%N A048200 Minimal length pair-exchange / set-rotate sequence to reverse n distinct ordered elements.
%C A048200 "Rotate" is always a left-rotate (moves leftmost element to the right end) and "Exchange" is always a pair-exchange of the two leftmost elements.
%C A048200 a(15)<=135 and a(16)<=160. See example solutions in the links section. - _Dmitry Kamenetsky_, Jun 19 2025
%H A048200 Danilo Bazzanella, Antonio Di Scala, Simone Dutto, and Nadir Murru, <a href="https://arxiv.org/abs/2002.08062">Primality tests, linear recurrent sequences and the Pell equation</a>, arXiv:2002.08062 [math.NT], 2020.
%H A048200 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a048/A048200.java">Java program</a> (github)
%H A048200 Dmitry Kamenetsky, <a href="/A048200/a048200.txt">Best known solutions for n <= 16.</a>
%H A048200 Sai Satwik Kuppili, <a href="/A048200/a048200_1.cpp.txt">C++ program for generating the moves for a given n</a>
%H A048200 Sai Satwik Kuppili and Bhadrachalam Chitturi, <a href="https://cs.utdallas.edu/wp-content/uploads/2019/09/LE.pdf">Exact upper bound for sorting R_n with LE</a>, University of Texas at Dallas (2019).
%H A048200 Sai Satwik Kuppili and Bhadrachalam Chitturi, <a href="https://arxiv.org/abs/2002.07342">An upper bound for sorting R_n with LRE</a>, arXiv:2002.07342 [cs.DS], 2020.
%H A048200 Sai Satwik Kuppili and Bhadrachalam Chitturi, <a href="https://doi.org/10.1142/S1793830920500330">Exact upper bound for sorting R_n with LE</a>, Discrete Mathematics, Algorithms and Applications, 2020.
%H A048200 Kevin Ryde, <a href="/A048200/a048200.c.txt">C Code</a>
%F A048200 Conjecture: a(n) = (3*n^2/4)-2*n if n is even and a(n) = (3*n^2-10*n+15)/4 if n is odd. See links for more information. - _Sai Satwik Kuppili_ and _Bhadrachalam Chitturi_, Jun 09 2020
%e A048200 a(4) = 4 since "xrrx" is the shortest sequence reversing "ABCD". Explicitly, (begin) ABCD, (x)-> BACD, (r)-> ACDB, (r) -> CDBA, (x)-> DCBA.
%o A048200 (Java) /* See links. */
%o A048200 (C) /* See links. */
%Y A048200 Cf. A058986, A065603, A186752.
%K A048200 nonn,nice,more
%O A048200 1,3
%A A048200 _Tony Bartoletti_
%E A048200 a(11) added by _Sai Satwik Kuppili_ and Srinath T, _Bhadrachalam Chitturi_, Jan 02 2019
%E A048200 a(12) from _Sean A. Irvine_, Jun 04 2021
%E A048200 a(13) from _Kevin Ryde_, Dec 19 2024
%E A048200 a(14) from _Zachary DeStefano_, Jan 03 2025