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%I #14 Jul 26 2013 11:26:14
%S 0,1,2,4,3,6,5,8,7,9,10,11,12,13,14,16,15,18,17,20,19,22,21,24,23,25,
%T 26,27,28,29,30,31,32,33,34,36,35,38,37,40,39,42,41,44,43,46,45,48,47,
%U 49,50,51,52,53,54,55,56,57,58,59,60,61,62,64,63,66,65,68,67
%N Permutation which maps between A227368 and A227369.
%C Conjecture 1: This is an involution (self-inverse permutation) of nonnegative integers. (Which would imply that both formulas given in A227368 and A227369 involving A227370 are valid).
%C Conjecture 2: (which would automatically imply the conjecture 1): the only transpositions (used to compose the permutation) are of adjacent terms 2k-1 and 2k, where A061887 gives the values of k. This is true at least for the first 35 transpositions (up to k=60).
%C See the example section of A227368 to get a grasp of the problem.
%H Antti Karttunen, <a href="/A227370/b227370.txt">Table of n, a(n) for n = 0..132</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) = A227183(A227369(n)).
%o (Scheme) (define (A227370 n) (A227183 (A227369 n)))
%Y Cf. A227368, A227369, A061887.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jul 08 2013
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