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 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 (list; graph; refs; listen; history; text; internal format)
 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 Amiram Eldar, Table of n, a(n) for n = 1..10000 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 Cf. A093653, A373092. Sequence in context: A131048 A119688 A126868 * A134187 A078644 A133700 Adjacent sequences: A373090 A373091 A373092 * A373094 A373095 A373096 KEYWORD nonn,easy,base AUTHOR Amiram Eldar, May 23 2024 STATUS approved

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Last modified August 11 23:45 EDT 2024. Contains 375082 sequences. (Running on oeis4.)