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

Author

Kevin Ryde, Jul 31 2022

Keywords

• nonn

Comments

A permutation of A111299.

Links

• 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

Crossrefs

Cf. A002024, A002260, A111299.

Programs

PARI

\\ See links.

Formula

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