A129593 Prime-factorization encoded partition codes for the Łukasiewicz-words in A071153.

1, 2, 4, 3, 8, 9, 9, 9, 5, 16, 27, 27, 6, 25, 27, 25, 6, 27, 25, 25, 25, 25, 7, 32, 81, 81, 18, 125, 81, 125, 18, 18, 15, 125, 15, 15, 49, 81, 125, 125, 15, 49, 18, 15, 18, 81, 125, 15, 125, 15, 49, 125, 49, 15, 125, 49, 15, 15, 125, 49, 49, 49, 49, 49, 11, 64, 243, 243, 54

Offset

0,2

Comments

If the signature-permutation of a Catalan automorphism SP satisfies the condition A129593(SP(n)) = A129593(n) for all n, then it is called a Łukasiewicz-word permuting automorphism. In addition to all the automorphisms whose signature permutation satisfies the more restricted condition A127301(SP(n)) = A127301(n) for all n, this includes also certain automorphisms like *A072797 that do not preserve the non-oriented form of the general tree. A000041(n) distinct values occur in each range [A014137(n-1)..A014138(n-1)]. All natural numbers occur. Cf. A129599.

Links

Antti Karttunen, Table of n, a(n) for n = 0..23713

Antti Karttunen, Scheme program for computing this sequence

OEIS Wiki, Łukasiewicz words

Index entries for sequences related to Łukasiewicz

Formula

Construction: remove zeros from the Łukasiewicz-word of a general plane tree encoded by A014486(n) (i.e. A071153(n)), sort the numbers into ascending order and interpreting it as a partition of a natural number, encode it in the manner explained in A129595.

For all i, j: A127301(i) = A127301(j) => a(i) = a(j). - Antti Karttunen, Apr 18 2026

Example

The terms A071153(5..7) are 201, 210 and 120. After discarding zero and sorting, each produces partition 1+2. Converting it to prime-exponents like explained in A129595, we get 2^0 * 3^2 = 9, thus a(5) = a(6) = a(7) = 9.

Prog

(Scheme) \\ See Links section.

Crossrefs

a(n) = a(A072797(n)).

Variant: A129599. To be computed: the position of the first and the last occurrence of n, the number of occurrences of each n.

Sequence in context: A332817 A332214 A285322 * A338619 A279355 A279356

Adjacent sequences: A129590 A129591 A129592 * A129594 A129595 A129596

Keyword

nonn

Author

Antti Karttunen, May 01 2007

Status

approved