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%I #16 Oct 25 2021 03:21:35
%S 1,2,3,4,5,7,6,8,15,12,9,16,11,14,29,17,10,35,13,30,33,22,26,36,71,28,
%T 82,34,21,73,18,37,55,25,72,83,27,32,69,74,20,80,24,56,183,66,52,84,
%U 79,180,63,70,31,197,144,81,77,54,19,184,65,43,194,85,176,146
%N Position within Beyer and Hedetniemi's rooted tree iteration (A346913) of the tree with Matula-Goebel number n.
%C This sequence is a permutation of the natural numbers, with inverse A347539.
%H Kevin Ryde, <a href="/A347540/b347540.txt">Table of n, a(n) for n = 1..7813</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e For n=21, the tree with Matula-Goebel number 21 is as follows, shown with siblings ordered per Beyer and Hedetniemi's canonical form,
%e root 1 pre-order levels = 1,2,3,3,2,3
%e | \ which is row 33 of A346913
%e level=2 2 2 so a(21) = 33
%e |\ |
%e level=3 3 3 3
%Y Cf. A346913, A347539 (inverse).
%K nonn
%O 1,2
%A _Kevin Ryde_, Sep 06 2021