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

Author

Joseph Myers, Aug 29 2009

Keywords

• base
• nonn

Examples

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

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..16384 (terms 0..1024 from Joseph Myers)
• Index entries for the Kaprekar map

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).

Programs

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 *)

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

Extensions

Cross-references edited by Joseph Myers, Sep 04 2009