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 A323596 #13 Jan 19 2019 03:50:34
%S A323596 1,3,3,3,1,2,1,-1,4,-1,1,3,5,-1,2,-1,1,-1,1,1,4,-1,-1,-1,-1,5,-1,-1,1,
%T A323596 4,-1,5,16,4,1,2,-1,3,1,14,-1,13,13,13,-1,12,1,-1,6,2,-1,-1,11,1,5,13,
%U A323596 -1,4,1,12,-1,-1,3,3,1,2,1,1,16,2,8,8,4,3,7,7,9,2,14
%N A323596 Number of (positive) iterations of f to reach an integer when starting from n/1. If no integer is ever reached then a(n) = -1. f(p/q) = (p + q) / (A000120(p) + A000120(q)).
%e A323596 8/1 -> 9/2 -> 11/3 -> 14/5 -> 19/5 -> 24/5 -> 29/4 -> 33/5 -> 38/4=19/2 -> 21/4 -> 25/4 -> 29/4 and the 5-cycle repeats, so a(8) = -1.
%e A323596 13/1 -> 14/4=7/2 -> 9/4 -> 13/3 -> 16/5 -> 21/3=7 so a(13) = 5.
%t A323596 Array[If[AnyTrue[#, IntegerQ], 1 + LengthWhile[#, ! IntegerQ@ # &], -1] &@ Rest@ NestWhileList[(#1 + #2)/(DigitCount[#1, 2, 1] + DigitCount[#2, 2, 1]) & @@ {Numerator@ #, Denominator@ #} &, #, UnsameQ, All] &, 79] (* _Michael De Vlieger_, Jan 18 2019 *)
%Y A323596 Cf. A000120, A058971, A059175, A323275, A323356, A323375.
%K A323596 sign
%O A323596 1,2
%A A323596 _Ctibor O. Zizka_, Jan 18 2019