cp's OEIS Frontend

A347620 Position of Matula-Goebel number n among Matula-Goebel numbers sorted by number of vertices then numerically as in A061773.

%I A347620 #18 Apr 01 2024 12:09:02
%S A347620 1,2,3,4,5,6,7,8,9,10,11,12,13,14,18,15,16,19,17,20,21,22,23,24,38,25,
%T A347620 39,26,27,40,28,29,41,30,42,43,31,32,44,45,33,46,34,47,86,48,49,50,51,
%U A347620 87,52,53,35,88,89,54,55,56,36,90,57,58,91,59,92,93,37,60
%N A347620 Position of Matula-Goebel number n among Matula-Goebel numbers sorted by number of vertices then numerically as in A061773.
%C A347620 This sequence is a permutation of the natural numbers, the inverse of A061773.
%C A347620 n = A005517(k) is the Matula-Goebel number of the first tree of k vertices so its position is immediately after all trees of 1..k-1 vertices so a(A005517(k)) = A087803(k-1) + 1.
%C A347620 n = A005518(k) is the last tree of k vertices so its position is a(A005518(k)) = A087803(k).
%H A347620 Kevin Ryde, <a href="/A347620/b347620.txt">Table of n, a(n) for n = 1..7813</a>
%H A347620 Kevin Ryde, <a href="/A347620/a347620.gp.txt">PARI/GP Code</a>.
%H A347620 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%H A347620 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A347620 a(n) = A087803(k-1) + s where s is the number of terms of A061775(1..n) equal to k, where k = A061775(n) is the number of vertices of n.
%e A347620 Tree n=25 is the first of 7 vertices (A005517(7)=25), so its position is after the A087803(6)=37 trees of 1..6 vertices so a(25) = 38.
%e A347620 Tree n=27 is the next of 7 vertices (has A061775(27)=7) so it is next after position 38: a(27) = 39.
%o A347620 (PARI) \\ See links.
%Y A347620 Cf. A061775 (number of vertices), A005517 (smallest), A005518 (largest), A087803 (number of trees).
%Y A347620 Cf. A061773 (inverse).
%Y A347620 Cf. A347540.
%K A347620 nonn
%O A347620 1,2
%A A347620 _Kevin Ryde_, Sep 09 2021