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Search: id:A093509
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| 0, 5, 6, 10, 12, 15, 18, 20, 24, 25, 30, 35, 36, 40, 42, 45, 48, 50, 54, 55, 60, 65, 66, 70, 72, 75, 78, 80, 84, 85, 90, 95, 96, 100, 102, 105, 108, 110, 114, 115, 120, 125, 126, 130, 132, 135, 138, 140, 144, 145, 150, 155, 156, 160, 162, 165, 168, 170, 174, 175
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Numbers that are congruent to {0, 5, 6, 10, 12, 15, 18, 20, 24, 25} mod 30.
Also without 0: numbers n such that cos(Pi*x/n)+cos(Pi*y/n)=1/2 has integer solutions (x,y).
Numbers n such that there exists a nontrivial configuration to an n-1 x n-1 Lights Out game from the all-off state to the all-off state.
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REFERENCES
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J. H. Conway and A. D. Jones, Trigonometric Diophantine equations (on vanishing sums of roots of unity), Acta Arith. XXX (1976) 229-240.
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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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FORMULA
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G.f.: x^2*(5-4*x+8*x^2-6*x^3+9*x^4-6*x^5+8*x^6-4*x^7+5*x^8) / ((x^4+x^3+x^2+x+1) * ( x^4-x^3+x^2-x+1) * (x-1)^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]
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EXAMPLE
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102 = 6*17, so 102 is in sequence.
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CROSSREFS
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Sequence in context: A037359 A099538 A093614 this_sequence A105953 A164095 A102506
Adjacent sequences: A093506 A093507 A093508 this_sequence A093510 A093511 A093512
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KEYWORD
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nonn,easy
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), May 22 2004
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EXTENSIONS
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G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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