

A373093


The fixed point of the iterations of the map x > A093653(x) that start at n.


2



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, 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, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 6, 3
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OFFSET

1,2


COMMENTS

Except for n = 1 and 2, all terms are either 3 or 6.
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, ... .


LINKS



EXAMPLE

The iterations for the n = 1..7 are:
n a(n) iterations
  
1 1 1
2 2 2
3 3 3
4 3 4 > 3
5 3 5 > 3
6 6 6
7 3 7 > 4 > 3


MATHEMATICA

d[n_] := DivisorSum[n, Plus @@ IntegerDigits[#, 2] &]; a[n_] := FixedPointList[d, n][[1]]; Array[a, 100]


PROG

(PARI) a(n) = {while(6 % n, n = sumdiv(n, d, hammingweight(d))); n; }


CROSSREFS



KEYWORD

nonn,easy,base


AUTHOR



STATUS

approved



