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%I #23 Aug 08 2023 03:21:45
%S 3,1,5,2,7,4,9,6,11,8,13,10,15,12,17,14,19,16,21,18,23,20,25,22,27,24,
%T 29,26,31,28,33,30,35,32,37,34,39,36,41,38,43,40,45,42,47,44,49,46,51,
%U 48,53,50,55,52,57,54,59,56,61,58,63,60,65,62,67,64,69,66,71,68,73,70
%N Permutation t->t-1 of Z, folded to N.
%C This permutation consists of just one cycle, which is infinite.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%F Let f: Z -> N be given by f(z) = 2z if z>0 else 2|z|+1, with inverse g(z) = z/2 if z even else (1-z)/2. Then a(n) = f(g(n)-1).
%F G.f.: x*(3-2*x+x^4+x^2-x^3) / ((x+1)*(x-1)^2). - _Alois P. Heinz_, Mar 07 2012
%F Sum_{n>=1} (-1)^n/a(n) = 2 - log(2). - _Amiram Eldar_, Aug 08 2023
%p a:= n-> n-2*(-1)^n +`if`(n=2, 1, 0):
%p seq(a(n), n=1..80); # _Alois P. Heinz_, Mar 07 2012
%t Join[{3, 1}, LinearRecurrence[{1, 1, -1}, {5, 2, 7}, 100]] (* _Jean-François Alcover_, Feb 28 2016 *)
%Y Inverse permutation to A065164.
%Y Obtained by composing permutations A065190 and A014681.
%K nonn,easy
%O 1,1
%A _Antti Karttunen_, Oct 19 2001
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