Reading along arithmetic progressions
Volume 80 / 1999
Colloquium Mathematicum 80 (1999), 293-296
DOI: 10.4064/cm-80-2-293-296
Abstract
Given a 0-1 sequence x in which both letters occur with density 1/2, do there exist arbitrarily long arithmetic progressions along which x reads 010101...? We answer the above negatively by showing that a certain regular triadic Toeplitz sequence does not have this property. On the other hand, we prove that if x is a generalized binary Morse sequence then each block can be read in x along some arithmetic progression.
