A309093 The analog of A309077(n), but allowing fractional powers.

1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12

Offset

1,2

Comments

Let x be a length-n binary word, and consider a factorization of the form prod_i w_i^{e_i}, where e_i can be any rational number. Here w^e means the prefix of www... of length e|w|. A factorization is minimal if the sum of the |w_i| is minimized, and this is called the (fractional) weight of the word x. Then a(n) is the maximum, over all length-n binary strings x, of the weight of x.

Links

Table of n, a(n) for n=1..20.

Example

For n = 10, the word 0010110010 has factorization 0 (01)^2 (100)^{5/3}, of weight 6.

Crossrefs

Cf. A309077, A309094.

Sequence in context: A066683 A055038 A276796 * A085268 A214656 A194979

Adjacent sequences: A309090 A309091 A309092 * A309094 A309095 A309096

Keyword

nonn,more

Author

Jeffrey Shallit, Jul 12 2019

Status

approved