A164886 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-2 Kaprekar map in A164884.

1, 2, 3, 2, 3, 3, 3, 2, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset

0,2

Comments

All base-2 cycles are fixed points, so one more than A164885.

Links

Joseph Myers, Table of n, a(n) for n = 0..1024

Index entries for the Kaprekar map

Mathematica

A164886[n_] := Length[FixedPointList[FromDigits[Reverse[#], 2] - FromDigits[#, 2] & [Sort[IntegerDigits[#, 2]]] &, n]] - 1;
Array[A164886, 100, 0] (* Paolo Xausa, Feb 05 2026 *)

Crossrefs

Cf. A164884, A163205, A164885, A164887.

In other bases: A164996 (base 3), A165015 (base 4), A165035 (base 5), A165054 (base 6), A165074 (base 7), A165093 (base 8), A165113 (base 9), A151963 (base 10).

Sequence in context: A076982 A351808 A283617 * A091935 A086063 A145653

Adjacent sequences: A164883 A164884 A164885 * A164887 A164888 A164889

Keyword

base,nonn

Author

Joseph Myers, Aug 29 2009

Extensions

Cross-references edited by Joseph Myers, Sep 04 2009

Status

approved