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 A373093 #11 May 24 2024 16:26:59
%S A373093 1,2,3,3,3,6,3,3,3,6,3,3,3,3,3,3,3,6,3,3,3,3,3,3,6,3,3,3,3,6,6,6,3,6,
%T A373093 3,3,3,3,6,3,3,6,3,3,3,6,6,3,3,3,3,3,3,6,3,3,6,6,6,3,6,3,3,3,3,3,3,3,
%U A373093 6,6,3,3,3,3,3,3,3,3,6,3,3,3,3,3,3,6,3
%N A373093 The fixed point of the iterations of the map x -> A093653(x) that start at n.
%C A373093 Except for n = 1 and 2, all terms are either 3 or 6.
%C A373093 Do the asymptotic densities of the occurrences of 3 and 6 exist? The numbers of occurrences of 6 for n that do not exceed 10^k, for k = 1, 2, ..., are 2, 24, 234, 2735, 25321, 242398, 2605532, 27441386, 268518855, 2561508455, ... .
%H A373093 Amiram Eldar, <a href="/A373093/b373093.txt">Table of n, a(n) for n = 1..10000</a>
%e A373093 The iterations for the n = 1..7 are:
%e A373093 n a(n) iterations
%e A373093 - ---- -----------
%e A373093 1 1 1
%e A373093 2 2 2
%e A373093 3 3 3
%e A373093 4 3 4 -> 3
%e A373093 5 3 5 -> 3
%e A373093 6 6 6
%e A373093 7 3 7 -> 4 -> 3
%t A373093 d[n_] := DivisorSum[n, Plus @@ IntegerDigits[#, 2] &]; a[n_] := FixedPointList[d, n][[-1]]; Array[a, 100]
%o A373093 (PARI) a(n) = {while(6 % n, n = sumdiv(n, d, hammingweight(d))); n;}
%Y A373093 Cf. A093653, A373092.
%K A373093 nonn,easy,base
%O A373093 1,2
%A A373093 _Amiram Eldar_, May 23 2024