|
%I #35 Sep 08 2022 08:44:33
%S 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,
%T 28,29,26,27,24,25,38,39,36,37,34,35,32,33,46,47,44,45,42,43,40,41,54,
%U 55,52,53,50,51,48,49,62,63
%N Nimsum n + 6.
%C A self-inverse permutation of the natural numbers. - _Philippe Deléham_, Nov 22 2016
%D E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 60.
%D J. H. Conway, On Numbers and Games. Academic Press, NY, 1976, pp. 51-53.
%H Vincenzo Librandi, <a href="/A004447/b004447.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Ni#Nimsums">Index entries for sequences related to Nim-sums</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-2,2,-1).
%F a(n) = n + 2*(-1)^floor(n/2) + 4*(-1)^floor(n/4). - Mitchell Harris, Jan 10 2005
%F 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
%t 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 *)
%t Table[BitXor[n, 6], {n, 0, 70}] (* _Bruno Berselli_, Nov 22 2016 *)
%t LinearRecurrence[{2,-2,2,-2,2,-2,2,-1},{6,7,4,5,2,3,0,1},70] (* _Harvey P. Dale_, Sep 30 2017 *)
%o (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
%o (Magma) [BitwiseXor(n, 6): n in [0..70]]; // _Bruno Berselli_, Nov 22 2016
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
|
