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

Author

Ludovic Schwob, Sep 21 2019

Keywords

• nonn
• hard
• more

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).

Examples

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

Crossrefs

Cf. A011784.

Extensions

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