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

1,2

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).

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

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.

Example

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.

Prog

(PARI) \\ See links.

Crossrefs

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

Cf. A061773 (inverse).

Cf. A347540.

Sequence in context: A302140 A039698 A377914 * A078107 A072089 A072088

Adjacent sequences: A347617 A347618 A347619 * A347621 A347622 A347623

Keyword

nonn

Author

Kevin Ryde, Sep 09 2021

Status

approved