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Beginning with the natural numbers, swap [ k*sqrt(5) ] and [ (k/4)*(5 + sqrt(5)) ], for all k >= 1.
7

%I #12 Mar 30 2012 18:56:05

%S 2,1,4,3,6,5,8,7,11,13,9,15,10,17,12,20,14,22,24,16,26,18,29,19,31,21,

%T 33,35,23,38,25,40,27,42,28,44,46,30,49,32,51,34,53,36,55,37,58,60,39,

%U 62,41,64,43,67,45,69,71,47,73,48,76,50,78

%N Beginning with the natural numbers, swap [ k*sqrt(5) ] and [ (k/4)*(5 + sqrt(5)) ], for all k >= 1.

%C Self-inverse integer permutation induced by Beatty sequences for sqrt(5) and (5+sqrt(5))/4. - _Reinhard Zumkeller_, Jun 11 2005

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>

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

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

%F a(A022839(n))=A108598(n) and a(A108598(n))=A022839(n). - _Reinhard Zumkeller_, Jun 11 2005

%Y Cf. A026250, A026255.

%K nonn

%O 1,1

%A _Clark Kimberling_