A165012 a(n) = image of n under the base-4 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order).

0, 0, 0, 0, 3, 0, 3, 6, 6, 3, 0, 3, 9, 6, 3, 0, 15, 15, 30, 45, 15, 0, 15, 30, 30, 15, 15, 30, 45, 30, 30, 30, 30, 30, 30, 45, 30, 15, 15, 30, 30, 15, 0, 15, 45, 30, 15, 15, 45, 45, 45, 45, 45, 30, 30, 30, 45, 30, 15, 15, 45, 30, 15, 0, 63, 75, 138, 201, 75, 63, 126, 189, 138, 126

Offset: 0

Author

Joseph Myers, Sep 04 2009

Keywords

• base
• nonn

Examples

			For n = 11, 11_10 = 23_4. So, a(11) = 32_4 - 23_4 = 14 - 11 = 3. - _Indranil Ghosh_, Feb 02 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. A165013.

In other bases: A164884 (base 2), A164993 (base 3), A165032 (base 5), A165051 (base 6), A165071 (base 7), A165090 (base 8), A165110 (base 9), A151949 (base 10).

Programs

Mathematica

b4km[n_]:=Module[{idn4=Sort[IntegerDigits[n,4]]},FromDigits[ Reverse[ idn4],4]-FromDigits[idn4,4]]; Array[b4km,80,0]

PARI

cons(m) = {local(b, r); r=0; b=1; for(i=1, matsize(m)[2], r=r+b*m[i]; b=b*4); r}
A165012(n) = {local(m, r); r=[]; m=n; while(m>0, r=concat(m%4, r); m=floor(m/4)); cons(vecsort(r,,0))-cons(vecsort(r,,4))} \\ Michael B. Porter, Nov 05 2009