OFFSET
2,4
COMMENTS
For each x in (0,1], let 1/2^p(1) + 1/2^p(2) + ... be the infinite binary representation of x. Let d(1) = p(1) and d(i) = p(i) - p(i-1) for i >=2. Call (d(i)) the powerdifference sequence of x, and denote it by D(x). Call m/n and u/v equivalent if every period of D(m/n) is a period of D(u/v). Define the binary fractility of n to be the number of distinct equivalence classes of {m/n: 0 < m < n}. Each class is represented by a minimal period, and a(n) is the length of the longest such period.
EXAMPLE
n classes a(n)
2 (1) 1
3 (2) 1
4 (1) 1
5 (1,3) 2
6 (1), (2) 1
7 (1,2), (3) 2
8 (1) 1
9 (1), (1,1,4) 3
10 (1), (1,3) 1
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 01 2016
STATUS
approved