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Search: id:A093614
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| A093614 |
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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. |
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+0
6
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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Goldwasser et al. proved that 2^k+-1 belongs to the set, for k>4.
Closed under multiplication by positive integers. - D. E. Knuth, May 11 2006
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REFERENCES
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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.
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LINKS
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M. Hunziker, A. Machiavelo and J. Park, Chebyshev polynomials over finite fields and reversibility of s-automata...
Eric Weisstein's World of Mathematics, Lights-Out Puzzle
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PROGRAM
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(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
(PARI) for(n=2, 200, t=F2(n):if(gcd(t, subst(t, x, 1-x))!=1, print1(n", ")))
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CROSSREFS
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Equals A117870(n) + 1.
Cf. A094425 (primitive elements), A076436.
Sequence in context: A046838 A037359 A099538 this_sequence A093509 A105953 A102506
Adjacent sequences: A093611 A093612 A093613 this_sequence A093615 A093616 A093617
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), May 22 2004
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