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%I #33 Sep 08 2022 08:44:33
%S 11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4,27,26,25,24,31,30,29,28,19,18,
%T 17,16,23,22,21,20,43,42,41,40,47,46,45,44,35,34,33,32,39,38,37,36,59,
%U 58,57,56,63,62,61,60,51,50,49,48,55,54,53,52,75,74,73
%N Nimsum n + 11.
%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="/A004452/b004452.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_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1,0,0,-1,1,0,0,1,-1).
%F a(n) = n + (-1)^n + 2*(-1)^floor(n/2) + 8*(-1)^floor(n/8). - Mitchell Harris, Jan 10 2005
%F G.f.: (11 - x - x^2 - x^3 - 4*x^4 - 5*x^8 - x^9 - x^10 - x^11 + 12*x^12)/((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^8)). - _Colin Barker_, Apr 12 2016
%F a(n) = A003987(n, 11). - _Michel Marcus_, Nov 10 2021
%t Table[BitXor[n, 11], {n, 0, 70}] (* _Bruno Berselli_, Nov 22 2016 *)
%o (PARI) Vec((11-x-x^2-x^3-4*x^4-5*x^8-x^9-x^10-x^11+12*x^12)/((1-x)^2*(1+x)*(1+x^2)*(1+x^8)) + O(x^50)) \\ _Colin Barker_, Apr 12 2016
%o (PARI) a(n) = n + (-1)^n + 2*(-1)^(n\2) + 8*(-1)^(n\8); \\ _Michel Marcus_, Apr 12 2016
%o (Magma) [BitwiseXor(n, 11): n in [0..70]]; // _Bruno Berselli_, Nov 22 2016
%o (Python)
%o def a(n): return n^11
%o print([a(n) for n in range(67)]) # _Michael S. Branicky_, Nov 10 2021
%Y Cf. A003987.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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