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%I #11 May 24 2024 16:26:59
%S 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 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 6,6,3,3,3,3,3,3,3,3,6,3,3,3,3,3,3,6,3
%N The fixed point of the iterations of the map x -> A093653(x) that start at n.
%C Except for n = 1 and 2, all terms are either 3 or 6.
%C 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 Amiram Eldar, <a href="/A373093/b373093.txt">Table of n, a(n) for n = 1..10000</a>
%e The iterations for the n = 1..7 are:
%e n a(n) iterations
%e - ---- -----------
%e 1 1 1
%e 2 2 2
%e 3 3 3
%e 4 3 4 -> 3
%e 5 3 5 -> 3
%e 6 6 6
%e 7 3 7 -> 4 -> 3
%t d[n_] := DivisorSum[n, Plus @@ IntegerDigits[#, 2] &]; a[n_] := FixedPointList[d, n][[-1]]; Array[a, 100]
%o (PARI) a(n) = {while(6 % n, n = sumdiv(n, d, hammingweight(d))); n;}
%Y Cf. A093653, A373092.
%K nonn,easy,base
%O 1,2
%A _Amiram Eldar_, May 23 2024
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