A327662 Length of shortest word of frequency depth n.

1, 2, 2, 3, 4, 5, 7, 10, 14, 21, 31, 45, 66, 99

Offset

1,2

Comments

The frequency depth of a word is the number of times one must take the multiset of multiplicities to reach the singleton (1), without rearranging it.

For example, the word (11213331) has frequency depth 7: (11213331) -> (21131) -> (1211) -> (112) -> (21) -> (11) -> (2) -> (1).

Links

Table of n, a(n) for n=1..14.

Example

The shortest words of frequency depth 10 are of the form (112122112112122122112) and (112122122112112122112), up to substitution and reflection.

Crossrefs

Cf. A011784.

Sequence in context: A032189 A316077 A186425 * A034395 A032232 A175306

Adjacent sequences: A327659 A327660 A327661 * A327663 A327664 A327665

Keyword

nonn,hard,more

Author

Ludovic Schwob, Sep 21 2019

Extensions

Incorrect terms removed by Samuel B. Reid, Aug 25 2021

Status

approved