A373093 The fixed point of the iterations of the map x -> A093653(x) that start at n.

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

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