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%I #30 Sep 08 2022 08:44:33
%S 12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3,28,29,30,31,24,25,26,27,20,21,
%T 22,23,16,17,18,19,44,45,46,47,40,41,42,43,36,37,38,39,32,33,34,35,60,
%U 61,62,63,56,57,58,59,52,53,54,55,48,49,50,51,76,77,78
%N Nimsum n + 12.
%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 Colin Barker, <a href="/A004453/b004453.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_14">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,-1,2,-1,0,-1,2,-1,0,-1,2,-1).
%F a(n) = n + 4*(-1)^floor(n/4) + 8*(-1)^floor(n/8). - Mitchell Harris, Jan 10 2005
%F G.f.: (12 - 11*x + 4*x^4 - 3*x^5 - 4*x^8 + 5*x^9 - 12*x^12 + 13*x^13)/((1 - x)^2*(1 + x^4)*(1 + x^8)). - _Colin Barker_, Apr 12 2016
%F a(n) = XOR(n, 12). - _Michel Marcus_, Apr 12 2016
%t Table[n + 4 (-1)^Floor[n / 4] + 8 (-1)^Floor[n / 8], {n, 0, 80}] (* _Vincenzo Librandi_, Nov 22 2016 *)
%o (PARI) Vec((12-11*x+4*x^4-3*x^5-4*x^8+5*x^9-12*x^12+13*x^13)/((1-x)^2*(1+x^4)*(1+x^8)) + O(x^50)) \\ _Colin Barker_, Apr 12 2016
%o (Magma) [BitwiseXor(n, 12): n in [0..70]]; // _Bruno Berselli_, Nov 22 2016
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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