A151949 -id:A151949 - cp's OEIS frontend

A164993 a(n) = image of n under the base-3 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order).

0, 0, 0, 2, 0, 2, 4, 2, 0, 8, 8, 16, 8, 0, 8, 16, 8, 8, 16, 16, 16, 16, 8, 8, 16, 8, 0, 26, 32, 58, 32, 26, 52, 58, 52, 58, 32, 26, 52, 26, 0, 26, 52, 26, 32, 58, 52, 58, 52, 26, 32, 58, 32, 26, 52, 58, 64, 58, 52, 58, 64, 58, 52, 58, 52, 58, 52, 26, 32, 58, 32, 26, 64, 58, 52, 58, 32

Offset: 0

Joseph Myers, Sep 04 2009

			For n = 10, 10_10 = 101_3. So, a(10) = 110_3 - 11_3 = 12 - 4 = 8. - _Indranil Ghosh_, Feb 02 2017

Indranil Ghosh, Table of n, a(n) for n = 0..19683 (terms 0..2187 from Joseph Myers)
Index entries for the Kaprekar map

Cf. A164994.

In other bases: A164884 (base 2), A165012 (base 4), A165032 (base 5), A165051 (base 6), A165071 (base 7), A165090 (base 8), A165110 (base 9), A151949 (base 10).

a[n_] := With[{dd = IntegerDigits[n, 3]}, FromDigits[ReverseSort[dd], 3] - FromDigits[Sort[dd], 3]];
a /@ Range[0, 100] (* Jean-François Alcover, Jan 08 2020 *)

A056965 a(n) = n - (reversal of digits of n).

Original entry on oeis.org

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

Offset: 0

Henry Bottomley, Jul 18 2000

a(n) is a multiple of 9.

			a(17) = 17 - 71 = -54.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for the Kaprekar map

Cf. A004086, A056964, A068396, A151949, A265326.

a056965 n = n - a004086 n  -- Reinhard Zumkeller, Sep 17 2013

a:= n-> (s-> n-parse(cat(s[-i]$i=1..length(s))))(""||n):
seq(a(n), n=0..82);  # Alois P. Heinz, Jul 11 2021

Table[n - FromDigits[Reverse[IntegerDigits[n]]], {n, 0, 82}] (* Jayanta Basu, Jul 11 2013 *)

a(n) = n - fromdigits(Vecrev(digits(n))); \\ Michel Marcus, Dec 20 2023

def a(n): return n - int(str(n)[::-1]) # Osman Mustafa Quddusi, Jul 11 2021

a(n) = n - A004086(n) = 2*n - A056964(n).

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).

Original entry on oeis.org

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

Joseph Myers, Aug 29 2009

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

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

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).

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 *)

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

Cross-references edited by Joseph Myers, Sep 04 2009

A164715 Length of cycle mentioned in A099010.

Original entry on oeis.org

2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 3, 7, 7, 3, 7, 7, 7, 7, 3, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 7, 3, 3, 7, 3, 7, 3, 3, 7, 7, 7, 7, 3, 3, 3, 3, 3, 3, 3, 8, 8, 5, 5, 8, 8, 8, 5, 5, 8, 8, 5, 8, 7, 3, 3, 3, 7, 3, 3, 3, 7, 3, 3, 3, 7, 7, 7, 7, 3

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..28910
Index entries for the Kaprekar map

Cf. A151949, A099010, A164717, A164719, A164721, A151966.

In other bases: Empty (base 2), A165001 (base 3), A165020 (base 4), A165040 (base 5), A165059 (base 6), A165079 (base 7), A165098 (base 8), A165118 (base 9). [From Joseph Myers, Sep 05 2009]

A164717 Length of cycle mentioned in A164716.

Original entry on oeis.org

1, 1, 1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 7, 1, 1, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 1, 3, 7, 7, 3, 7, 7, 7, 7, 3, 1, 1, 14, 14, 14, 14, 14, 1, 14, 14, 14, 14, 14, 14, 14, 14, 14, 7, 1, 3, 3, 7, 3, 7, 3, 3, 7, 7, 7, 7, 3, 3, 3, 3, 3, 1, 3, 3, 1, 8, 8, 5, 1, 5, 8, 8, 8, 5, 5, 8, 8, 5, 8, 7, 1, 1, 3

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..29572
Index entries for the Kaprekar map

Cf. A151949, A164716, A164715, A164719, A164721, A151966.

In other bases: A000012 (base 2), A164999 (base 3), A165018 (base 4), A165038 (base 5), A165057 (base 6), A165077 (base 7), A165096 (base 8), A165116 (base 9). [From Joseph Myers, Sep 05 2009]

A164719 Length of cycle mentioned in A164718.

Original entry on oeis.org

1, 1, 1, 2, 4, 4, 7, 1, 1, 8, 7, 1, 3, 1, 1, 14, 1, 7, 1, 3, 3, 3, 3, 1, 1, 8, 5, 1, 7, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 1, 1, 5, 1, 5, 2, 5, 7, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 1, 1, 5, 1, 5, 2, 5, 5, 5, 7, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..10163
Index entries for the Kaprekar map

Cf. A151949, A164718, A164715, A164717, A164721, A151966.

In other bases: A000012 (base 2), A165003 (base 3), A165022 (base 4), A165042 (base 5), A165061 (base 6), A165081 (base 7), A165100 (base 8), A165120 (base 9). [From Joseph Myers, Sep 05 2009]

A164721 Length of cycle mentioned in A164720.

Original entry on oeis.org

2, 4, 4, 7, 8, 7, 3, 14, 7, 3, 3, 3, 3, 8, 5, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 2, 5, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 2, 5, 5, 5, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 2, 5, 5, 5, 5, 7, 3, 3

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..9501
Index entries for the Kaprekar map

Cf. A151949, A164720, A164715, A164717, A164719, A151966.

In other bases: Empty (base 2), A165005 (base 3), A165024 (base 4), A165044 (base 5), A165063 (base 6), A165083 (base 7), A165102 (base 8), A165122 (base 9). [From Joseph Myers, Sep 05 2009]

A227362 Distinct digits of n arranged in decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 21, 31, 41, 51, 61, 71, 81, 91, 20, 21, 2, 32, 42, 52, 62, 72, 82, 92, 30, 31, 32, 3, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 4, 54, 64, 74, 84, 94, 50, 51, 52, 53, 54, 5, 65, 75, 85, 95, 60, 61, 62, 63, 64, 65, 6, 76, 86

Offset: 0

Reinhard Zumkeller, Jul 09 2013

a(n) <= 9876543210; a(a(n)) = a(n);
A055642(a(n)) <= 10;
A055642(a(n)) <= A055642(n), A055642(a(n)) = A055642(n) iff A178788(n) = 1;
a(A109303(n)) < A109303(n); a(A009995(n)) = A009995(n); a(A071589(n)) > A071589(n);
a(n) = A151949(n) + A180410(n).

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A004186, A230959.

import Data.List (nub, sort)
a227362 = read . reverse . sort . nub . show :: Integer -> Integer

a:= n-> parse(cat(sort([{convert(n, base, 10)[]}[]], `>`)[])):
seq(a(n), n=0..68);  # Alois P. Heinz, Sep 21 2022

f[n_] := FromDigits[Reverse@ Union@ IntegerDigits@ n]; f /@ Range[0, 68] (* Michael De Vlieger, Apr 16 2015, corrected by Robert G. Wilson v *)

a(n) = {if (n == 0, d = [0], d = digits(n)); eval(subst(Pol(vecsort(d,,12)), x, 10));} \\ Michel Marcus, Apr 16 2015

a(n)=fromdigits(vecsort(digits(n),,12)) \\ Charles R Greathouse IV, Apr 16 2015

def A227362(n): return int(''.join(sorted(set(str(n)),reverse=True))) # Chai Wah Wu, Nov 23 2022

A180410 Unique digits used in n in numerical order.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 12, 13, 14, 15, 16, 17, 18, 19, 2, 12, 2, 23, 24, 25, 26, 27, 28, 29, 3, 13, 23, 3, 34, 35, 36, 37, 38, 39, 4, 14, 24, 34, 4, 45, 46, 47, 48, 49, 5, 15, 25, 35, 45, 5, 56, 57, 58, 59, 6, 16, 26, 36, 46, 56, 6, 67, 68, 69, 7

Offset: 1

Dominick Cancilla, Sep 02 2010

a(n) = A227362(n) - A151949(n). - Reinhard Zumkeller, Jul 09 2013

			a(93077) = 0379 = 379. Seven is only used once and the digits are sorted. The initial zero is not shown.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

This is identical to A180409 with the zeros removed.

import Data.List (nub, sort)
a180410 = read . sort . nub . show :: Integer -> Integer
-- Reinhard Zumkeller, Jul 09 2013

a:= n-> parse(cat(sort([{convert(n, base, 10)[]}[]])[])):
seq(a(n), n=1..70);  # Alois P. Heinz, Sep 21 2022

a(n) = 0123456789 after any digits not appearing in n are removed.

A108782 Difference between n and the largest number with the same digit set as n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 18, 27, 36, 45, 54, 63, 72, 0, 0, 0, 9, 18, 27, 36, 45, 54, 63, 0, 0, 0, 0, 9, 18, 27, 36, 45, 54, 0, 0, 0, 0, 0, 9, 18, 27, 36, 45, 0, 0, 0, 0, 0, 0, 9, 18, 27, 36, 0, 0, 0, 0, 0, 0, 0, 9, 18, 27, 0, 0, 0, 0, 0, 0, 0, 0, 9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0

Offset: 0

Zak Seidov, Jun 29 2005

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A004186, A151949, A193581.

FromDigits[Sort[IntegerDigits[n], Greater]] - n (Rob Pratt)
Table[Max[FromDigits/@ Permutations[IntegerDigits[n]]]-n, {n, 150}]

a(n) = A004186(n) - n. - Seiichi Manyama, Sep 25 2018

a(0)=0 prepended by Seiichi Manyama, Sep 25 2018

cp's OEIS Frontend

A164993 a(n) = image of n under the base-3 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order).

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A056965 a(n) = n - (reversal of digits of n).

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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).

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A164715 Length of cycle mentioned in A099010.

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A164717 Length of cycle mentioned in A164716.

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A164719 Length of cycle mentioned in A164718.

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A164721 Length of cycle mentioned in A164720.

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A227362 Distinct digits of n arranged in decreasing order.

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Haskell

Maple

Mathematica

PARI

PARI

Python

A180410 Unique digits used in n in numerical order.

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