%I #6 Aug 17 2024 13:57:00
%S 1,2,3,5,4,7,6,8,11,9,12,10,15,16,13,14,17,18,23,24,19,20,25,26,21,22,
%T 31,32,33,34,27,28,29,30,35,36,37,38,47,48,49,50,39,40,41,42,51,52,53,
%U 54,43,44,45,46,63,64,65,66,67,68,69,70,55,56,57,58,59,60
%N Let X be the sequence of power towers built of 2's and 3's, sorted first by their height and then colexicographically: 2, 3, 2^2, 3^2, 2^3, 3^3, 2^2^2, 3^2^2, etc. Sequence gives the permutation of indices which reorders X by magnitude.
%C The terms are less dispersed here compared to A185969, because colex order is more correlated to the magnitude of the power tower than lex order is, i.e., we often get a smaller value of the power tower by putting the small numbers high up in the tower. Specifically, the only integers x, y >= 2 for which x < y and x^y < y^x is x = 2, y = 3.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%F a(2*n-1) = 2*a(n-1)+1 and a(2*n) = a(2*n-1)+1 for n >= 7.
%F a(n) = A081241(A185969(n)).
%Y 3rd row of A375376.
%Y Cf. A081241, A185969 (lexicographic instead of colexicographic order), A375375 (inverse permutation).
%K nonn
%O 1,2
%A _Pontus von Brömssen_, Aug 13 2024