A373092 The number of iterations of the map x -> A093653(x) that are required to reach from n to one of the fixed points, 1, 2, 3 or 6.

0, 0, 0, 1, 1, 0, 2, 2, 2, 1, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 3, 3, 2, 4, 1, 3, 3, 4, 2, 3, 1, 1, 3, 1, 3, 4, 2, 3, 2, 4, 2, 3, 2, 4, 4, 2, 1, 4, 3, 4, 3, 4, 2, 3, 3, 3, 2, 2, 1, 4, 1, 4, 2, 3, 3, 3, 2, 3, 2, 3, 2, 4, 2, 3, 3, 4, 3, 4, 1, 4, 4, 3, 2, 4, 3, 2, 4

Offset

1,7

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    0   1
  2    0   2
  3    0   3
  4    1   4 -> 3
  5    1   5 -> 3
  6    0   6
  7    2   7 -> 4 -> 3

Mathematica

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

Prog

(PARI) a(n) = {my(c = 0); while(6 % n, n = sumdiv(n, d, hammingweight(d)); c++); c; }

Crossrefs

Cf. A086793 (decimal analog), A093653, A373093, A373094.

Sequence in context: A006371 A000177 A319815 * A222656 A162545 A162544

Adjacent sequences: A373089 A373090 A373091 * A373093 A373094 A373095

Keyword

nonn,easy,base

Author

Amiram Eldar, May 23 2024

Status

approved