A165110 -id:A165110 - cp's OEIS frontend

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

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

A165128 Smallest member of cycle corresponding to n-th term of A165127.

Original entry on oeis.org

0, 16, 320, 2256, 3712, 34960, 41520, 183696, 3496800, 31596672, 31531872, 278474880, 326952560, 2066242576, 2516902752, 2598744000, 26531651360, 23087388720, 167365651216, 203869268832, 211282856832, 2184410558000

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 9: 0, 17, 385, 3076, 5074, 52854, 62853, 308876, 6518633, 65407433.

Joseph Myers, Table of n, a(n) for n=1..1560
Index entries for the Kaprekar map

Cf. A165110, A165115, A165127, A165129.

In other bases: A163205 (base 2), A165010 (base 3), A165030 (base 4), A165049 (base 5), A165069 (base 6), A165088 (base 7), A165108 (base 8), A151965 (base 10).

A165129 Length of cycle corresponding to n-th term of A165127.

Original entry on oeis.org

1, 2, 2, 3, 3, 5, 1, 14, 2, 4, 1, 12, 1, 5, 4, 1, 6, 1, 6, 2, 2, 4, 6, 1, 11, 1, 1, 3, 4, 6, 1, 2, 1, 7, 1, 2, 1, 9, 6, 1, 1, 4, 4, 1, 1, 1, 15, 6, 1, 1, 6, 4, 7, 4, 1, 1, 10, 2, 2, 2, 1, 8, 3, 2, 7, 4, 1, 1, 1, 1, 2, 6, 1, 1, 3, 2, 6, 4, 6, 7, 3, 2, 8, 3, 7, 4, 1, 1, 1, 2, 13, 1, 1, 20, 4, 5, 1, 2, 3, 6, 2, 8

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..1560
Index entries for the Kaprekar map

Cf. A165110, A165115, A165127, A165128.

In other bases: A000012 (base 2), A165011 (base 3), A165031 (base 4), A165050 (base 5), A165070 (base 6), A165089 (base 7), A165109 (base 8), A151966 (base 10).

A165116 Length of cycle mentioned in A165115.

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 1, 5, 5, 5, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 2, 2, 1, 4, 4, 4, 4, 12, 12, 12, 1, 12, 12, 12, 12, 12, 12, 12, 12, 12, 5, 5, 4, 5, 5, 1, 4, 4, 5, 4, 1, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 2, 6, 2, 2, 6, 1, 6, 6, 4, 6, 4, 6, 4, 6, 4, 6, 11, 11

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..7826
Index entries for the Kaprekar map

Cf. A165110, A165115, A165118, A165120, A165122, A165129.

In other bases: A000012 (base 2), A164999 (base 3), A165018 (base 4), A165038 (base 5), A165057 (base 6), A165077 (base 7), A165096 (base 8), A164717 (base 10).

A165118 Length of cycle mentioned in A165117.

Original entry on oeis.org

2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 2, 2, 4, 4, 4, 4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 5, 5, 4, 5, 5, 4, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 2, 6, 2, 2, 6, 6, 6, 4, 6, 4, 6, 4, 6, 4, 6, 11, 11, 11, 11, 11, 11, 11

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..7548
Index entries for the Kaprekar map

Cf. A165110, A165117, A165116, A165120, A165122, A165129.

In other bases: Empty (base 2), A165001 (base 3), A165020 (base 4), A165040 (base 5), A165059 (base 6), A165079 (base 7), A165098 (base 8), A164715 (base 10).

A165120 Length of cycle mentioned in A165119.

Original entry on oeis.org

1, 2, 2, 3, 3, 5, 1, 14, 2, 1, 4, 12, 1, 5, 4, 1, 1, 6, 6, 2, 2, 1, 6, 4, 11, 1, 1, 1, 3, 6, 4, 2, 1, 1, 2, 7, 1, 6, 9, 1, 1, 1, 4, 1, 4, 1, 6, 15, 1, 1, 1, 4, 6, 7, 4, 1, 10, 1, 2, 2, 2, 1, 1, 1, 8, 3, 2, 7, 4, 1, 6, 1, 2, 1, 1, 1, 7, 4, 6, 3, 6, 3, 2, 8, 3, 2, 7, 4, 1, 13, 1, 1, 2, 1, 2, 20, 1, 5, 4, 6, 3, 2

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..1560
Anthony Kay and Katrina Downes-Ward, Fixed Points and Cycles of the Kaprekar Transformation: 1. Odd Bases, Journal of Integer Sequences, Vol. 25 (2022), Article 22.6.7.
Index entries for the Kaprekar map

Cf. A165110, A165119, A165116, A165118, A165122, A165129.

In other bases: A000012 (base 2), A165003 (base 3), A165022 (base 4), A165042 (base 5), A165061 (base 6), A165081 (base 7), A165100 (base 8), A164719 (base 10).

A165122 Length of cycle mentioned in A165121.

Original entry on oeis.org

2, 2, 3, 3, 5, 14, 2, 4, 12, 5, 4, 6, 6, 2, 2, 6, 4, 11, 3, 6, 4, 2, 2, 7, 6, 9, 4, 4, 6, 15, 4, 6, 7, 4, 10, 2, 2, 2, 8, 3, 2, 7, 4, 6, 2, 7, 4, 6, 3, 6, 3, 2, 8, 3, 2, 7, 4, 13, 2, 2, 20, 5, 4, 6, 3, 2, 8, 3, 2, 7, 4, 31, 6, 3, 7, 5, 8, 5, 4, 6, 3, 2, 8, 3, 2, 7, 4, 7, 22, 7, 3, 8, 5, 7, 5, 8, 5, 4, 6, 3, 2

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..1282
Index entries for the Kaprekar map

Cf. A165110, A165121, A165116, A165118, A165120, A165129.

In other bases: Empty (base 2), A165005 (base 3), A165024 (base 4), A165044 (base 5), A165063 (base 6), A165083 (base 7), A165102 (base 8), A164721 (base 10).

A319657 Write n in 9-ary, sort digits into increasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 1, 10, 11, 12, 13, 14, 15, 16, 17, 2, 11, 20, 21, 22, 23, 24, 25, 26, 3, 12, 21, 30, 31, 32, 33, 34, 35, 4, 13, 22, 31, 40, 41, 42, 43, 44, 5, 14, 23, 32, 41, 50, 51, 52, 53, 6, 15, 24, 33, 42, 51, 60, 61, 62, 7, 16, 25, 34, 43, 52, 61, 70, 71

Offset: 0

Seiichi Manyama, Sep 25 2018

Seiichi Manyama, Table of n, a(n) for n = 0..6560

b-ary: A038573 (b=2), A038574 (b=3), A319652 (b=4), A319653 (b=5), A319654 (b=6), A319655 (b=7), A319656 (b=8), this sequence (b=9), A004185 (b=10).

Cf. A165110.

a:= n-> (l-> add(l[-i]*9^(i-1), i=1..nops(l)))(sort(convert(n, base, 9))):
seq(a(n), n=0..71);  # Alois P. Heinz, Aug 07 2024

Table[FromDigits[Sort[IntegerDigits[n, 9]], 9], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = fromdigits(vecsort(digits(n, 9)), 9); \\ Michel Marcus, Sep 25 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.join.to_i(k)}
end
p A(9, 100)

A319726 Write n in 9-ary, sort digits into decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 28, 37, 46, 55, 64, 73, 18, 19, 20, 29, 38, 47, 56, 65, 74, 27, 28, 29, 30, 39, 48, 57, 66, 75, 36, 37, 38, 39, 40, 49, 58, 67, 76, 45, 46, 47, 48, 49, 50, 59, 68, 77, 54, 55, 56, 57, 58, 59, 60, 69, 78, 63, 64, 65, 66, 67, 68, 69

Offset: 0

Seiichi Manyama, Sep 26 2018

Seiichi Manyama, Table of n, a(n) for n = 0..6560

b-ary: A073138 (b=2), A319651 (b=3), A319720 (b=4), A319722 (b=5), A319723 (b=6), A319724 (b=7), A319725 (b=8), this sequence (b=9), A004186 (b=10).

Cf. A165110, A319657.

Table[FromDigits[Reverse[Sort[IntegerDigits[n,9]]],9],{n,0,70}] (* Harvey P. Dale, Oct 26 2022 *)

a(n) = fromdigits(vecsort(digits(n, 9), , 4), 9); \\ Michel Marcus, Sep 26 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.reverse.join.to_i(k)}
end
p A(9, 100)

n <= a(n) < 9n. - Charles R Greathouse IV, Aug 07 2024

A319747 a(n) = A319726(n) + A319657(n).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 10, 20, 30, 40, 50, 60, 70, 80, 90, 20, 30, 40, 50, 60, 70, 80, 90, 100, 30, 40, 50, 60, 70, 80, 90, 100, 110, 40, 50, 60, 70, 80, 90, 100, 110, 120, 50, 60, 70, 80, 90, 100, 110, 120, 130, 60, 70, 80, 90, 100, 110, 120, 130, 140, 70

Offset: 0

Seiichi Manyama, Sep 27 2018

This sequence is different from A055958. For example, A055958(82) = 164 and a(82) = 100.

Seiichi Manyama, Table of n, a(n) for n = 0..6560

Base b: A319785 (b=2), this sequence (b=9), A052008 (b=10).

Cf. A055958, A165110, A319657, A319726.

Table[FromDigits[Reverse[#], 9] + FromDigits[#, 9] & [Sort[IntegerDigits[n, 9]]], {n, 0, 100}] (* Paolo Xausa, Aug 08 2024 *)

a(n) = my(dn=digits(n, 9)); fromdigits(vecsort(dn), 9) + fromdigits(vecsort(dn,,4), 9); \\ Michel Marcus, Sep 28 2018

cp's OEIS Frontend

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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A165128 Smallest member of cycle corresponding to n-th term of A165127.

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A165129 Length of cycle corresponding to n-th term of A165127.

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A165116 Length of cycle mentioned in A165115.

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A165118 Length of cycle mentioned in A165117.

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A165120 Length of cycle mentioned in A165119.

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A165122 Length of cycle mentioned in A165121.

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A319657 Write n in 9-ary, sort digits into increasing order.

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A319726 Write n in 9-ary, sort digits into decreasing order.

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A319747 a(n) = A319726(n) + A319657(n).

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