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Beginning with the natural numbers, swap [ k*sqrt(2) ] and [ k*(2 + sqrt(2)) ], for all k >= 1.
8

%I #14 Feb 22 2013 21:36:40

%S 3,6,1,10,13,2,17,20,23,4,27,30,5,34,37,40,7,44,47,8,51,54,9,58,61,64,

%T 11,68,71,12,75,78,81,14,85,88,15,92,95,16,99,102,105,18,109,112,19,

%U 116,119,122,21,126,129,22,133,136,139,24,143,146

%N Beginning with the natural numbers, swap [ k*sqrt(2) ] and [ k*(2 + sqrt(2)) ], for all k >= 1.

%C Self-inverse integer permutation induced by Beatty sequences for sqrt(2) and 2+sqrt(2). - _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(A001951(n)) = A001952(n) and a(A001952(n)) = A001951(n). - _Reinhard Zumkeller_, Jun 11 2005

%Y Cf. A026255, A026262.

%K nonn

%O 1,1

%A _Clark Kimberling_