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A345717 Orders of abelian cubes in the tribonacci word A080843. 1
4, 6, 7, 11, 13, 17, 18, 20, 24, 26, 27, 30, 31, 33, 37, 38, 40, 41, 42, 43, 44, 48, 50, 51, 55, 57, 61, 62, 63, 64, 68, 70, 74, 75, 77, 79, 81, 85, 86, 87, 88, 92, 94, 95, 98, 99, 101, 105, 107, 108, 111, 112, 114, 116, 118, 119, 122, 123, 125, 129, 131, 132 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
An abelian cube is a word of the form x x' x'', where x' and x'' are permutations of x, like the English word "deeded". The order of an abelian cube is the length of x.
LINKS
FORMULA
There is a deterministic finite automaton of 1169 states that takes n in its tribonacci representation as input and accepts if and only if there is an abelian cube of order n. It can be obtained with the Walnut theorem-prover.
EXAMPLE
Here are the earliest-appearing abelian cubes of the first few orders:
n = 4: 2010.0102.0102
n = 6: 102010.010201.010201
n = 7: 0102010.0102010.1020100
n = 11: 02010010201.01020100102.01020100102
CROSSREFS
Cf. A080843.
Sequence in context: A287157 A102140 A047289 * A022436 A102139 A167228
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jun 24 2021
STATUS
approved

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Last modified June 15 19:43 EDT 2024. Contains 373410 sequences. (Running on oeis4.)