This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A269571 #16 Sep 20 2019 19:36:59
%S A269571 2,3,4,5,8,11,13,16,19,29,32,37,53,59,61,64,67,83,101,107,128,131,139,
%T A269571 149,163,173,179,181,197,211,227,256,269,293,317,347,349,373,379,389,
%U A269571 419,421,443,461,467,491,509,512,523,541,547,557,563,587,613,619
%N A269571 Numbers having binary fractility 1.
%C A269571 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}.
%H A269571 Robert Price, <a href="/A269571/b269571.txt">Table of n, a(n) for n = 1..76</a>
%e A269571 D(1/5) = (3,1,3,1,3,1,3,1,...)
%e A269571 D(2/5) = (2,1,3,1,3,1,3,1,...)
%e A269571 D(3/5) = (1,3,1,3,1,3,1,3,...)
%e A269571 D(4/5) = (1,1,3,1,3,1,3,1,...).
%e A269571 This shows that all m/5, for 0<m<5 are equivalent to 1/5, so that there is only 1 equivalence class.
%t A269571 A269570[n_] := CountDistinct[With[{l = NestWhileList[
%t A269571 Rescale[#, {1/2^(Floor[-Log[2, #]] + 1),
%t A269571 1/2^(Floor[-Log[2, #]])}] &, #, UnsameQ, All]},
%t A269571 Min@l[[First@First@Position[l, Last@l] ;;]]] & /@
%t A269571 Range[1/n, 1 - 1/n, 1/n]] (* from Davin Park, Nov 19 2016 *)
%t A269571 Select[Range[1000], A269570[#] == 1 &] (* _Robert Price_, Sep 20 2019 *)
%Y A269571 Cf. A269570, A269572.
%K A269571 nonn
%O A269571 1,1
%A A269571 _Clark Kimberling_, Mar 01 2016
%E A269571 Corrected Offset by _Robert Price_, Sep 20 2019
%E A269571 a(37)-a(56) from _Robert Price_, Sep 20 2019