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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.
2
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
1,1
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.
Sequence in context: A041054 A297980 A120034 * A078981 A041555 A041747
KEYWORD
nonn,hard,more
AUTHOR
Ralf Stephan, May 22 2004
EXTENSIONS
Gebhardt and Sutner references from Don Knuth, May 11 2006
STATUS
approved