A004450 - OEIS

%I #30 Sep 08 2022 08:44:33

%S 9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6,25,24,27,26,29,28,31,30,17,16,

%T 19,18,21,20,23,22,41,40,43,42,45,44,47,46,33,32,35,34,37,36,39,38,57,

%U 56,59,58,61,60,63,62,49,48,51,50,53,52,55,54,73,72,75

%N Nimsum n + 9.

%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="/A004450/b004450.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_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,0,0,-1,1,1,-1).

%F a(n) = n + (-1)^n + 8*(-1)^floor(n/8). - Mitchell Harris, Jan 10 2005

%F G.f.: (9 - x - 6*x^2 - 7*x^8 - x^9 + 10*x^10)/((1 - x)^2*(1 + x)*(1 + x^8)). - _Colin Barker_, Apr 12 2016

%F a(n) = n XOR 9. - _Michel Marcus_, Apr 12 2016

%t Table[BitXor[n, 2], {n, 0, 70}] (* _Bruno Berselli_, Nov 22 2016 *)

%t LinearRecurrence[{1,1,-1,0,0,0,0,-1,1,1,-1},{9,8,11,10,13,12,15,14,1,0,3},100] (* _Harvey P. Dale_, May 09 2018 *)

%o (PARI) Vec((9-x-6*x^2-7*x^8-x^9+10*x^10)/((1-x)^2*(1+x)*(1+x^8)) + O(x^50)) \\ _Colin Barker_, Apr 12 2016

%o (Magma) [BitwiseXor(n, 9): n in [0..70]]; // _Bruno Berselli_, Nov 22 2016

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_