%I #6 May 02 2017 22:17:15

%S 1,6,2,12,4,10,3,24,8,14,7,20,5,18,11,48,16,22,15,28,13,26,19,40,9,30,

%T 23,36,21,34,27,96,32,38,31,44,29,42,35,56,25,46,39,52,37,50,43,80,17,

%U 54,47,60,45,58,51,72,41,62,55,68,53,66,59,192,64,70,63,76,61,74,67,88

%N Permutation of Z, folded to N, corresponding to the site swap pattern ...242824202428242... (A065176).

%C This permutation corresponds to the site swap pattern shown in the figure 7 of Buhler and Graham paper and consists of one fixed point (at 0, mapped here to 1) and infinite number of infinite cycles.

%H Joe Buhler and R. L. Graham, <a href="http://www.cecm.sfu.ca/organics/papers/buhler/index.html">Juggling Drops and Descents</a>, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%p [seq(Z2N(N2Z(n)+TZ2(abs(N2Z(n)))), n=1..120)]; TZ2 := proc(xx) local x,s; s := 1; x := xx; if(0 = x) then RETURN(0); fi; while(0 = (x mod 2)) do x := floor(x/2); s := s+1; od; RETURN(2^s); end;

%p N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1),1,0);

%Y Inverse permutation: A065175. A065176 gives the deltas p(t)-t, i.e. the associated site swap sequence. Cf. also A065167, A065171.

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 19 2001