A164884 a(n) = image of n under the base-2 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order).

0, 0, 1, 0, 3, 3, 3, 0, 7, 9, 9, 7, 9, 7, 7, 0, 15, 21, 21, 21, 21, 21, 21, 15, 21, 21, 21, 15, 21, 15, 15, 0, 31, 45, 45, 49, 45, 49, 49, 45, 45, 49, 49, 45, 49, 45, 45, 31, 45, 49, 49, 45, 49, 45, 45, 31, 49, 45, 45, 31, 45, 31, 31, 0, 63, 93, 93, 105, 93, 105, 105, 105, 93, 105, 105

Offset

0,5

Links

Indranil Ghosh, Table of n, a(n) for n = 0..16384 (terms 0..1024 from Joseph Myers)

Index entries for the Kaprekar map

Example

For n = 17, 17_10 = 10001_2. So, a(17) = 11000_2 - 11_2 = 24 - 3 = 21. - Indranil Ghosh, Feb 01 2017

Mathematica

a[n_] := With[{dd = IntegerDigits[n, 2]}, FromDigits[ReverseSort[dd], 2] - FromDigits[Sort[dd], 2]];
a /@ Range[0, 100] (* Jean-François Alcover, Jan 08 2020 *)

Prog

(Python)
def A164884(n):
    return int("".join(sorted(bin(n)[2:], reverse=True)), 2)-int("".join(sorted(bin(n)[2:])), 2) # Indranil Ghosh, Feb 01 2017

Crossrefs

Cf. A163205, A164885, A164886, A164887.

In other bases: A164993 (base 3), A165012 (base 4), A165032 (base 5), A165051 (base 6), A165071 (base 7), A165090 (base 8), A165110 (base 9), A151949 (base 10).

Sequence in context: A126660 A202698 A320785 * A357073 A019801 A086634

Adjacent sequences: A164881 A164882 A164883 * A164885 A164886 A164887

Keyword

base,nonn

Author

Joseph Myers, Aug 29 2009

Extensions

Cross-references edited by Joseph Myers, Sep 04 2009

Status

approved