A151949 - OEIS

A151949

a(n) = image of n under the 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, 0, 0, 9, 0, 9, 18, 27, 36, 45, 54, 63, 72, 18, 9, 0, 9, 18, 27, 36, 45, 54, 63, 27, 18, 9, 0, 9, 18, 27, 36, 45, 54, 36, 27, 18, 9, 0, 9, 18, 27, 36, 45, 45, 36, 27, 18, 9, 0, 9, 18, 27, 36, 54, 45, 36, 27, 18, 9, 0, 9, 18, 27, 63, 54, 45, 36, 27, 18, 9, 0, 9, 18, 72, 63, 54, 45, 36, 27, 18, 9, 0, 9, 81, 72, 63, 54, 45, 36, 27, 18, 9, 0, 99, 99, 198, 297, 396, 495, 594, 693, 792, 891, 99, 0, 99, 198, 297, 396, 495, 594, 693, 792

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OFFSET

0,11

COMMENTS

Entries are multiples of 9 - see A151950.

a(n) = A004186(n) - A004185(n); a(A010785(n)) = 0. - Reinhard Zumkeller, corrected: Mar 23 2015, Jul 09 2013

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..20000 (terms 0..1000 from Joseph Myers and Robert G. Wilson v)

H. Hanslik, E. Hetmaniok, I. Sobstyl, et al., Orbits of the Kaprekar's transformations-some introductory facts, Zeszyty Naukowe Politechniki Śląskiej, Seria: Matematyka Stosowana z. 5, Nr kol. 1945; 2015.

M. Kauers and C. Koutschan, Some D-finite and some possibly D-finite sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023.

R. J. Mathar, Maple code for A151949 and A151959

Joseph Myers, C program for computing sequences related to the Kaprekar map

Joseph Myers, List of cycles under Kaprekar map (all numbers with <= 60 digits; cycles are represented by their smallest value)

Index entries for the Kaprekar map

EXAMPLE

For n = 15, a(15) = 51 - 15 = 36. - Indranil Ghosh, Feb 01 2017

MATHEMATICA

f[n_] := Module[{idn = IntegerDigits@n, idns}, idns = Sort@ idn; FromDigits@ Reverse@ idns - FromDigits@ idns]; Table[ f@n, {n, 0, 200}] (* Harvey P. Dale, Aug 18 2009 *)

Flatten[Table[Differences[FromDigits /@ {y = Sort[x = IntegerDigits[n]], Reverse[y]}], {n, 0, 74}]] (* Jayanta Basu, Jul 11 2013 *)

PROG

(Haskell)

a151949 n = a004186 n - a004185 n

-- Reinhard Zumkeller, corrected: Mar 23 2015, Jul 09 2013

(Python)

def A151949(n):

return int("".join(sorted(str(n), reverse=True)))-int("".join(sorted(str(n)))) # Indranil Ghosh, Feb 01 2017

(PARI) a(n) = {my(d=digits(n)); fromdigits(vecsort(d, , 4)) - fromdigits(vecsort(d)); } \\ Michel Marcus, Dec 08 2019

CROSSREFS

In other bases: A164884 (base 2), A164993 (base 3), A165012 (base 4), A165032 (base 5), A165051 (base 6), A165071 (base 7), A165090 (base 8), A165110 (base 9). - Joseph Myers, Sep 05 2009

Cf. A151959, A069746, A347688.

Cf. also A004185, A004186, A099009 (fixed points).

Sequence in context: A332093 A056965 A347688 * A341486 A349825 A320379

Adjacent sequences: A151946 A151947 A151948 * A151950 A151951 A151952

KEYWORD

nonn,base,look

AUTHOR

N. J. A. Sloane, Aug 18 2009

EXTENSIONS

More terms from Robert G. Wilson v, Aug 19 2009

More than the usual number of terms are shown in order to distinguish this from similar sequences. - N. J. A. Sloane, Sep 22 2021

STATUS

approved