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.

EXAMPLE

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

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Jul 12 2019

STATUS

approved