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A054082 Permutation of N: a(1)=2, a(2)=1 and for each k >= 2, let p(k)=least natural number not already an a(i), q(k)=p(k)+k-1, a(2k-1)=q(k), a(2k)=p(k).

%I A054082 #10 Apr 01 2020 09:55:56
%S A054082 2,1,4,3,7,5,9,6,12,8,15,10,17,11,20,13,22,14,25,16,28,18,30,19,33,21,
%T A054082 36,23,38,24,41,26,43,27,46,29,49,31,51,32,54,34,56,35,59,37,62,39,64,
%U A054082 40,67,42,70,44,72,45,75,47,77,48,80,50,83
%N A054082 Permutation of N: a(1)=2, a(2)=1 and for each k >= 2, let p(k)=least natural number not already an a(i), q(k)=p(k)+k-1, a(2k-1)=q(k), a(2k)=p(k).
%H A054082 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t A054082 a[n_] := If[OddQ[n], Floor[((n+1)/2 - 1) GoldenRatio] + (n+1)/2 + 1, Floor[(n/2 - 1) GoldenRatio] + 2]; a[2] = 1;
%t A054082 Array[a, 100] (* _Jean-François Alcover_, Apr 01 2020 *)
%Y A054082 Odd-indexed terms: A026356. Even-indexed terms: A026355. Inverse permutation: A064579.
%K A054082 nonn,eigen
%O A054082 1,1
%A A054082 _Clark Kimberling_