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.

5, 6, 17, 31, 33, 63, 127, 129, 171, 257, 511, 683, 2047, 2731, 2979, 3277, 3641, 8191, 28197, 43691, 48771, 52429, 61681, 65537, 85489, 131071

Offset: 1

Author

Ralf Stephan, May 22 2004

Keywords

• nonn
• hard
• more

Comments

Klaus Sutner, Jun 26 2006, remarks that it can be shown that this sequence is infinite.

References

• Dieter Gebhardt, "Cross pattern puzzles revisited," Cubism For Fun 69 (March 2006), 23-25.

Links

• K. Sutner, Linear cellular automata and the Garden-of-Eden, Math. Intelligencer, 11 (No. 2, 1989), 49-53.
• K. Sutner, The computational complexity of cellular automata, in Lect. Notes Computer Sci., 380 (1989), 451-459.
• K. Sutner, sigma-Automata and Chebyshev-polynomials, Theoretical Comp. Sci., 230 (2000), 49-73.
• M. Hunziker, A. Machiavelo and J. Park, Chebyshev polynomials over finite fields and reversibility of sigma-automata on square grids, Theoretical Comp. Sci., 320 (2004), 465-483.
• Eric Weisstein's World of Mathematics, Lights-Out Puzzle

Crossrefs

Cf. A093614 (all elements), A076436.

Extensions

Gebhardt and Sutner references from Don Knuth, May 11 2006