A356121 Matula-Goebel number of the rooted binary tree with Colijn-Plazzotta number n.

1, 4, 14, 49, 86, 301, 1849, 454, 1589, 9761, 51529, 886, 3101, 19049, 100561, 196249, 3986, 13951, 85699, 452411, 882899, 3972049, 31754, 111139, 682711, 3604079, 7033511, 31642861, 252079129, 6418, 22463, 137987, 728443, 1421587, 6395537, 50949293, 10297681

Offset

1,2

Comments

A permutation of A111299.

Links

Table of n, a(n) for n=1..37.

C. Colijn and G. Plazzotta, A Metric on Phylogenetic Tree Shapes, Systematic Biology, volume 67, number 1, January 2018, pages 113-126.

F. Goebel, On a 1-1-Correspondence between Rooted Trees and Natural Numbers, Journal of Combinatorial Theory, series B, volume 29, 1980, pages 141-143.

D. W. Matula, A Natural Rooted Tree Enumeration By Prime Factorization, SIAM Review, volume 10, number 2, April 1968, page 273 (also at JSTOR).

Kevin Ryde, PARI/GP Code

Index entries for sequences related to Matula-Goebel numbers

Formula

a(n) = prime(a(x)) * prime(a(y)) for n>=2, where subtrees x = A002024(n-1) and y = A002260(n-1).

Prog

(PARI) \\ See links.

Crossrefs

Cf. A002024, A002260, A111299.

Sequence in context: A363468 A111299 A245824 * A345326 A327610 A110686

Adjacent sequences: A356118 A356119 A356120 * A356122 A356123 A356124

Keyword

nonn,changed

Author

Kevin Ryde, Jul 31 2022

Status

approved