On the Exact Height of Integer-Detecting Sequences Original Research Article

Some time ago, the concept of integer-detecting sequences of exact heightξwas introduced. So far all the occurring exact heights were rational numbers, in fact even unit fractions. Otherwise it was known that 0<ξless-than-or-equals, slant1/3. We show that every positive real number not exceeding 1/3 is the exact height of some integer-detecting sequence and discuss some examples.