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

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, 39, 26, 27, 40, 28, 29, 41, 30, 42, 43, 31, 32, 44, 45, 33, 46, 34, 47, 86, 48, 49, 50, 51, 87, 52, 53, 35, 88, 89, 54, 55, 56, 36, 90, 57, 58, 91, 59, 92, 93, 37, 60

Offset: 1

Author

Kevin Ryde, Sep 09 2021

Keywords

• nonn

Comments

This sequence is a permutation of the natural numbers, the inverse of A061773.

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.

n = A005518(k) is the last tree of k vertices so its position is a(A005518(k)) = A087803(k).

Examples

			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.
Tree n=27 is the next of 7 vertices (has A061775(27)=7) so it is next after position 38: a(27) = 39.
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..7813
• Kevin Ryde, PARI/GP Code.
• Index entries for sequences related to Matula-Goebel numbers
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A061775 (number of vertices), A005517 (smallest), A005518 (largest), A087803 (number of trees).

Cf. A061773 (inverse).

Cf. A347540.

Programs

PARI

\\ See links.

Formula

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.