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A185969 Let S be the sequence of power towers built of 2 and 3 sorted by their height and for equal heights - in lexicographic order: 2, 3, 2^2, 2^3, 3^2, 3^3, 2^2^2, 2^2^3 etc. A(n) = the permutation of indexes which reorders S by magnitude.

%I A185969 #39 Dec 23 2024 14:53:42
%S A185969 1,2,3,4,5,7,6,11,8,9,12,13,15,23,10,14,19,27,16,24,17,25,20,28,21,29,
%T A185969 31,47,39,55,18,26,22,30,35,51,43,59,32,48,40,56,33,49,41,57,36,52,44,
%U A185969 60,37,53,45,61,63,95,79,111,71,103,87,119,34,50,42,58,38
%N A185969 Let S be the sequence of power towers built of 2 and 3 sorted by their height and for equal heights - in lexicographic order: 2, 3, 2^2, 2^3, 3^2, 3^3, 2^2^2, 2^2^3 etc. A(n) = the permutation of indexes which reorders S by magnitude.
%H A185969 Alois P. Heinz, <a href="/A185969/b185969.txt">Table of n, a(n) for n = 1..14335</a>
%H A185969 Vladimir Reshetnikov, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-March/014595.html">2-3 sequence puzzle</a>, SeqFan list, Mar 18 2015
%H A185969 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A185969 a(2*n-1) = A081241(2*A081241(a(n-1))+1) and a(2*n) = A081241(A081241(a(2*n-1))+1) for n >= 7. - _Pontus von Brömssen_, Aug 10 2024
%e A185969 a(6) =  7; tower(7)  = 2^2^2 = 2^4 =  16.
%e A185969 a(7) =  6; tower(6)  = 3^3   =        27.
%e A185969 a(8) = 11; tower(11) = 3^2^2 = 3^4 =  81.
%e A185969 a(9) =  8; tower(8)  = 2^2^3 = 2^8 = 256.
%Y A185969 Cf. A032810, A081241, A248907, A256179, A256231, A375374 (colexicographic instead of lexicographic order).
%K A185969 nonn,look
%O A185969 1,2
%A A185969 _Vladimir Reshetnikov_, Feb 07 2011
%E A185969 More terms from _Alois P. Heinz_, Apr 05 2011