

A093614


Numbers n such that F_n(x) and F_n(1x) have a common factor mod 2, with F_n(x) = U(n1,x/2) the monic Chebyshev polynomials of second kind.


6



5, 6, 10, 12, 15, 17, 18, 20, 24, 25, 30, 31, 33, 34, 35, 36, 40, 42, 45, 48, 50, 51, 54, 55, 60, 62, 63, 65, 66, 68, 70, 72, 75, 78, 80, 84, 85, 90, 93, 95, 96, 99, 100, 102, 105, 108, 110, 114, 115, 119, 120, 124, 125, 126, 127, 129, 130, 132, 135, 136, 138
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OFFSET

1,1


COMMENTS

Goldwasser et al. proved that 2^k+1 belongs to the set, for k>4.
Closed under multiplication by positive integers.  Don Knuth, May 11 2006


LINKS

Ralf Stephan and Thomas Buchholz, Table of n, a(n) for n = 1..1000 [terms 1 through 61 were computed by Ralf Stephan, May 22 2004; terms 62 through 1000 by Thomas Buchholz, May 16 2014]
M. Hunziker, A. Machiavelo and J. Park, Chebyshev polynomials over finite fields and reversibility of sigmaautomata on square grids, Theoretical Comp. Sci., 320 (2004), 465483.
K. Sutner, Linear cellular automata and the GardenofEden, Math. Intelligencer, 11 (No. 2, 1989), 4953.
K. Sutner, The computational complexity of cellular automata, in Lect. Notes Computer Sci., 380 (1989), 451459.
Eric Weisstein's World of Mathematics, LightsOut Puzzle


PROG

(PARI)
{ F2(n)=local(t, t1, t2, tmp); t1=Mod(0, 2); t2=Mod(1, 2); t=Mod(1, 2)*x; for(k=2, n, tmp=t*t2t1; t1=t2; t2=tmp); tmp }
for(n=2, 200, t=F2(n); if(gcd(t, subst(t, x, 1x))!=1, print1(n", ")))


CROSSREFS

Equals A117870(n) + 1.
Cf. A094425 (primitive elements), A076436.
Sequence in context: A326418 A037359 A099538 * A093509 A105953 A164095
Adjacent sequences: A093611 A093612 A093613 * A093615 A093616 A093617


KEYWORD

nonn


AUTHOR

Ralf Stephan, May 22 2004


EXTENSIONS

More terms from Thomas Buchholz, May 16 2014


STATUS

approved



