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A093614 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. 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 (list; graph; refs; listen; history; text; internal format)
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 sigma-automata on square grids, Theoretical Comp. Sci., 320 (2004), 465-483.

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.

Eric Weisstein's World of Mathematics, Lights-Out 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*t2-t1; t1=t2; t2=tmp); tmp }

for(n=2, 200, t=F2(n); if(gcd(t, subst(t, x, 1-x))!=1, print1(n", ")))

CROSSREFS

Equals A117870(n) + 1.

Cf. A094425 (primitive elements), A076436.

Sequence in context: A046838 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

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Last modified February 23 05:58 EST 2019. Contains 320411 sequences. (Running on oeis4.)