A165090 a(n) is the image of n under the base-8 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order).

0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 14, 21, 28, 35, 42, 14, 7, 0, 7, 14, 21, 28, 35, 21, 14, 7, 0, 7, 14, 21, 28, 28, 21, 14, 7, 0, 7, 14, 21, 35, 28, 21, 14, 7, 0, 7, 14, 42, 35, 28, 21, 14, 7, 0, 7, 49, 42, 35, 28, 21, 14, 7, 0, 63, 63, 126, 189, 252, 315, 378, 441, 63, 0, 63, 126, 189

Offset: 0

Author

Joseph Myers, Sep 04 2009

Keywords

• base
• nonn

Examples

			For n = 11, 11_10 = 13_8. So, a(11) = 31_8 - 13_8 = 25 - 11 = 14. - _Indranil Ghosh_, Feb 02 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..32768 (terms 0..4096 from Joseph Myers)
• Index entries for the Kaprekar map

Crossrefs

Cf. A165091.

In other bases: A164884 (base 2), A164993 (base 3), A165012 (base 4), A165032 (base 5), A165051 (base 6), A165071 (base 7), A165110 (base 9), A151949 (base 10).

Programs

Mathematica

a[n_] := With[{dd = IntegerDigits[n, 8]}, FromDigits[ReverseSort[dd], 8] - FromDigits[Sort[dd], 8]];
a /@ Range[0, 100] (* Jean-François Alcover, Jan 08 2020 *)

Python

def A165090(n):
    if n==0:return 0
    return int("".join(sorted(oct(n)[2:],reverse=True)),8)-int("".join(sorted(oct(n)[2:])),8) # Indranil Ghosh, Feb 02 2017