cp's OEIS Frontend

A117870 Square board sizes for which the lights out problem does not have a unique solution (counting solutions differing only by rotation and reflection as distinct).

%I A117870 #26 Feb 16 2025 08:33:00
%S A117870 4,5,9,11,14,16,17,19,23,24,29,30,32,33,34,35,39,41,44,47,49,50,53,54,
%T A117870 59,61,62,64,65,67,69,71,74,77,79,83,84,89,92,94,95,98,99,101,104,107,
%U A117870 109,113,114,118,119,123,124,125,126,128,129,131,134,135,137,139,143
%N A117870 Square board sizes for which the lights out problem does not have a unique solution (counting solutions differing only by rotation and reflection as distinct).
%C A117870 Numbers k such that a k X k parity pattern exists (see A118141). - _Don Knuth_, May 11 2006
%H A117870 Max Alekseyev and Thomas Buchholz, <a href="/A117870/b117870.txt">Table of n, a(n) for n = 1..1000</a> [terms were extended by Max Alekseyev, Sep 17 2009; terms 64 through 1000 were computed by Thomas Buchholz, May 16 2014]
%H A117870 Jaap's puzzle page, <a href="http://www.jaapsch.net/puzzles/lomath.htm">The Mathematics of Lights Out</a>
%H A117870 K. Sutner, <a href="http://dx.doi.org/10.1007/BF03023823">Linear cellular automata and the Garden-of-Eden</a>, Math. Intelligencer, 11 (No. 2, 1989), 49-53.
%H A117870 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LightsOutPuzzle.html">Lights-Out Puzzle</a>
%H A117870 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lights_Out_(game)">Lights Out (game)</a>
%F A117870 a(n) = A093614(n) - 1.
%F A117870 Contains positive integers k such that A159257(k) > 0. - _Max Alekseyev_, Sep 17 2009
%Y A117870 Cf. A075462, A076437, A117872. Complement of A076436.
%K A117870 nonn
%O A117870 1,1
%A A117870 _N. J. A. Sloane_, May 14 2006
%E A117870 More terms from _Max Alekseyev_, Sep 17 2009, and _Thomas Buchholz_, May 16 2014