cp's OEIS Frontend

A094425 Numbers n such that F_n(x) and F_n(1-x) have a common factor mod 2, with F_n(x) = U(n-1,x/2) the monic Chebyshev polynomials of second kind; this lists only the primitive elements of the set.

%I A094425 #16 Feb 16 2025 08:32:53
%S A094425 5,6,17,31,33,63,127,129,171,257,511,683,2047,2731,2979,3277,3641,
%T A094425 8191,28197,43691,48771,52429,61681,65537,85489,131071
%N A094425 Numbers n such that F_n(x) and F_n(1-x) have a common factor mod 2, with F_n(x) = U(n-1,x/2) the monic Chebyshev polynomials of second kind; this lists only the primitive elements of the set.
%C A094425 Klaus Sutner, Jun 26 2006, remarks that it can be shown that this sequence is infinite.
%D A094425 Dieter Gebhardt, "Cross pattern puzzles revisited," Cubism For Fun 69 (March 2006), 23-25.
%H A094425 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 A094425 K. Sutner, <a href="http://dx.doi.org/10.1007/3-540-51498-8_44">The computational complexity of cellular automata</a>, in Lect. Notes Computer Sci., 380 (1989), 451-459.
%H A094425 K. Sutner, <a href="http://dx.doi.org/10.1016/S0304-3975(97)00242-9">sigma-Automata and Chebyshev-polynomials</a>, Theoretical Comp. Sci., 230 (2000), 49-73.
%H A094425 M. Hunziker, A. Machiavelo and J. Park, <a href="http://dx.doi.org/10.1016/j.tcs.2004.03.031">Chebyshev polynomials over finite fields and reversibility of sigma-automata on square grids</a>, Theoretical Comp. Sci., 320 (2004), 465-483.
%H A094425 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LightsOutPuzzle.html">Lights-Out Puzzle</a>
%Y A094425 Cf. A093614 (all elements), A076436.
%K A094425 nonn,hard,more
%O A094425 1,1
%A A094425 _Ralf Stephan_, May 22 2004
%E A094425 Gebhardt and Sutner references from _Don Knuth_, May 11 2006