cp's OEIS Frontend

A375374 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.

%I A375374 #6 Aug 17 2024 13:57:00
%S A375374 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 A375374 31,32,33,34,27,28,29,30,35,36,37,38,47,48,49,50,39,40,41,42,51,52,53,
%U A375374 54,43,44,45,46,63,64,65,66,67,68,69,70,55,56,57,58,59,60
%N A375374 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 A375374 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 A375374 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%F A375374 a(2*n-1) = 2*a(n-1)+1 and a(2*n) = a(2*n-1)+1 for n >= 7.
%F A375374 a(n) = A081241(A185969(n)).
%Y A375374 3rd row of A375376.
%Y A375374 Cf. A081241, A185969 (lexicographic instead of colexicographic order), A375375 (inverse permutation).
%K A375374 nonn
%O A375374 1,2
%A A375374 _Pontus von Brömssen_, Aug 13 2024