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%I #21 Jan 19 2023 11:05:08
%S 16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,
%T 10,11,12,13,14,15,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,32,
%U 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,80,81,82,83,84,85,86,87,88,89,90
%N Nimsum n + 16.
%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="/A004457/b004457.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_18">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,2,-1).
%F a(n) = n + 16(-1)^[n/16]. - Mitchell Harris, Jan 10 2005
%F From _Colin Barker_, Apr 13 2016: (Start)
%F a(n) = n XOR 16.
%F G.f.: (16-15*x-16*x^16+17*x^17) / ((1-x)^2*(1+x^16)).
%F (End)
%p f:=n->n+16*(-1)^floor(n/16);
%o (PARI) Vec((16-15*x-16*x^16+17*x^17)/((1-x)^2*(1+x^16)) + O(x^50)) \\ _Colin Barker_, Apr 13 2016
%o (Python)
%o def A004457(n): return n^16 # _Chai Wah Wu_, Jan 19 2023
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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