cp's OEIS Frontend

A269572 Maximal period-length associated with binary fractility of n.

%I A269572 #7 Nov 24 2016 16:40:56
%S A269572 1,1,1,2,1,2,1,3,2,5,1,6,2,3,1,4,3,9,2,4,5,7,1,10,6,9,2,14,3,4,1,5,4,
%T A269572 7,3,18,9,8,2,10,4,7,5,7,7,14,1,11,10,6,6,26,9,12,2,9,14,29,3,30,4,5,
%U A269572 1,6,5,33,4,11,7,21,3,6,18,11,9,15,8,22,2,27
%N A269572 Maximal period-length associated with binary fractility of n.
%C A269572 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.
%e A269572 n        classes          a(n)
%e A269572 2         (1)              1
%e A269572 3         (2)              1
%e A269572 4         (1)              1
%e A269572 5         (1,3)            2
%e A269572 6         (1), (2)         1
%e A269572 7         (1,2), (3)       2
%e A269572 8         (1)              1
%e A269572 9         (1), (1,1,4)     3
%e A269572 10        (1), (1,3)       1
%Y A269572 Cf. A269570, A269571.
%K A269572 nonn,easy
%O A269572 2,4
%A A269572 _Clark Kimberling_, Mar 01 2016