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6, 7, 4, 5, 2, 3, 0, 1, 14, 15, 12, 13, 10, 11, 8, 9, 22, 23, 20, 21, 18, 19, 16, 17, 30, 31, 28, 29, 26, 27, 24, 25, 38, 39, 36, 37, 34, 35, 32, 33, 46, 47, 44, 45, 42, 43, 40, 41, 54, 55, 52, 53, 50, 51, 48, 49, 62, 63
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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A self-inverse permutation of the natural numbers. - Philippe Deléham, Nov 22 2016
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REFERENCES
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E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 60.
J. H. Conway, On Numbers and Games. Academic Press, NY, 1976, pp. 51-53.
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LINKS
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FORMULA
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a(n) = n + 2*(-1)^floor(n/2) + 4*(-1)^floor(n/4). - Mitchell Harris, Jan 10 2005
G.f.: (7*x^7 - 6*x^6 + 3*x^5 - 2*x^4 - x^3 + 2*x^2 - 5*x + 6)/((x - 1)^2*(x^2 + 1)*(x^4 + 1)). - Colin Barker, Jun 29 2014
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MATHEMATICA
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CoefficientList[Series[(7 x^7 - 6 x^6 + 3 x^5 - 2 x^4 - x^3 + 2 x^2 - 5 x + 6)/((x - 1)^2 (x^2 + 1) (x^4 + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 30 2014 *)
LinearRecurrence[{2, -2, 2, -2, 2, -2, 2, -1}, {6, 7, 4, 5, 2, 3, 0, 1}, 70] (* Harvey P. Dale, Sep 30 2017 *)
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PROG
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(PARI) Vec((7*x^7-6*x^6+3*x^5-2*x^4-x^3+2*x^2-5*x+6)/((x-1)^2*(x^2+1)*(x^4+1)) + O(x^100)) \\ Colin Barker, Jun 29 2014
(Magma) [BitwiseXor(n, 6): n in [0..70]]; // Bruno Berselli, Nov 22 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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