A165100 -id:A165100 - cp's OEIS frontend

A165099 Consider the base-8 Kaprekar map n->K(n) defined in A165090. Sequence gives least elements of each cycle, including fixed points.

0, 21, 252, 1022, 1589, 17892, 21483, 102837, 147420, 213402, 1445787, 1707930, 1711962, 6589877, 13667738, 16092433, 76545756, 93093147, 110132442, 111443346, 421817781, 874802586, 878996762, 1029991697, 1068263553

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 8: 0, 25, 374, 1776, 3065, 42744, 51753, 310665, 437734, 640632.

Joseph Myers, Table of n, a(n) for n=1..8775
Anthony Kay and Katrina Downes-Ward, Fixed Points and Cycles of the Kaprekar Transformation: 2. Even bases, arXiv:2408.12257 [math.CO], 2024. See p. 33.
Index entries for the Kaprekar map

Union of A165094 and A165101. Cf. A165090, A165100, A165095, A165097, A165108, A165103.

In other bases: A163205 (base 2), A165002 (base 3), A165021 (base 4), A165041 (base 5), A165060 (base 6), A165080 (base 7), A165119 (base 9), A164718 (base 10).

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]

A165003 Length of cycle mentioned in A165002.

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 1, 3, 2, 1, 4, 1, 3, 1, 3, 2, 1, 2, 1, 5, 3, 1, 3, 2, 1, 1, 2, 1, 6, 5, 3, 1, 3, 2, 1, 3, 1, 2, 1, 4, 2, 1, 6, 5, 3, 1, 3, 2, 1, 5, 3, 1, 2, 1, 4, 4, 4, 2, 1, 6, 5, 3, 1, 3, 2, 1, 3, 1, 3, 1, 2, 1, 9, 4, 4, 4, 2, 1, 6, 5, 3, 1, 3, 2, 1, 2, 3, 1, 3, 1, 2, 1, 6, 3, 1, 9, 4, 4, 4, 2, 1, 6, 5, 3, 1

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..23340
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. A164993, A165002, A164999, A165001, A165005, A165011.

In other bases: A000012 (base 2), A165022 (base 4), A165042 (base 5), A165061 (base 6), A165081 (base 7), A165100 (base 8), A165120 (base 9), A164719 (base 10).

A165022 Length of cycle mentioned in A165021.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..7165
Anthony Kay and Katrina Downes-Ward, Fixed Points and Cycles of the Kaprekar Transformation: 2. Even bases, arXiv:2408.12257 [math.CO], 2024. See p. 16.
Index entries for the Kaprekar map

Cf. A165012, A165021, A165018, A165020, A165024, A165031.

In other bases: A000012 (base 2), A165003 (base 3), A165042 (base 5), A165061 (base 6), A165081 (base 7), A165100 (base 8), A165120 (base 9), A164719 (base 10).

A165042 Length of cycle mentioned in A165041.

Original entry on oeis.org

1, 1, 2, 1, 4, 5, 4, 6, 1, 4, 3, 1, 8, 5, 3, 1, 5, 4, 4, 6, 2, 5, 3, 1, 5, 4, 1, 4, 2, 2, 4, 6, 2, 5, 3, 1, 5, 1, 3, 4, 4, 4, 4, 4, 2, 2, 4, 6, 2, 5, 3, 1, 3, 1, 9, 9, 3, 4, 4, 4, 4, 4, 2, 2, 4, 6, 2, 5, 3, 1, 5, 5, 3, 1, 6, 6, 2, 6, 3, 3, 1, 9, 9, 3, 4, 4, 4, 4, 4, 2, 2, 4, 6, 2, 5, 3, 1, 11, 5, 3, 1, 11, 11

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..15716
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. A165032, A165041, A165038, A165040, A165044, A165050.

In other bases: A000012 (base 2), A165003 (base 3), A165022 (base 4), A165061 (base 6), A165081 (base 7), A165100 (base 8), A165120 (base 9), A164719 (base 10).

A165061 Length of cycle mentioned in A165060.

Original entry on oeis.org

1, 1, 6, 2, 1, 3, 1, 1, 1, 2, 7, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..23045
Anthony Kay and Katrina Downes-Ward, Fixed Points and Cycles of the Kaprekar Transformation: 2. Even bases, arXiv:2408.12257 [math.CO], 2024. See p. 27.
Index entries for the Kaprekar map

Cf. A165051, A165060, A165057, A165059, A165063, A165070.

In other bases: A000012 (base 2), A165003 (base 3), A165022 (base 4), A165042 (base 5), A165081 (base 7), A165100 (base 8), A165120 (base 9), A164719 (base 10).

A165081 Length of cycle mentioned in A165080.

Original entry on oeis.org

1, 2, 3, 5, 6, 6, 6, 11, 2, 2, 2, 1, 2, 5, 6, 1, 1, 9, 2, 2, 1, 1, 1, 2, 12, 1, 2, 1, 1, 1, 2, 4, 1, 2, 1, 2, 1, 1, 1, 2, 5, 7, 2, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 1, 1, 2, 5, 1, 2, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 1, 1, 1, 2, 5, 5, 1, 1, 2, 1, 2, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 1, 1, 1, 2, 24, 1, 1, 1, 2

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..13070
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. A165071, A165080, A165077, A165079, A165083, A165089.

In other bases: A000012 (base 2), A165003 (base 3), A165022 (base 4), A165042 (base 5), A165061 (base 6), A165100 (base 8), A165120 (base 9), A164719 (base 10).

A165096 Length of cycle mentioned in A165095.

Original entry on oeis.org

1, 1, 1, 5, 3, 5, 5, 3, 5, 3, 5, 2, 2, 4, 4, 4, 4, 3, 1, 3, 1, 3, 7, 7, 7, 4, 1, 7, 4, 7, 7, 7, 4, 4, 3, 3, 3, 3, 3, 3, 1, 1, 5, 5, 4, 4, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 6, 4, 6, 4, 2, 6, 6, 4, 2, 4, 6, 6, 3, 1, 3, 3, 3, 3, 3, 3, 4, 1, 3, 2, 3, 3, 3, 3, 1, 4, 4, 3, 3, 3, 4, 2

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..25797
Index entries for the Kaprekar map

Cf. A165090, A165095, A165098, A165100, A165102, A165109.

In other bases: A000012 (base 2), A164999 (base 3), A165018 (base 4), A165038 (base 5), A165057 (base 6), A165077 (base 7), A165116 (base 9), A164717 (base 10).

A165098 Length of cycle mentioned in A165097.

Original entry on oeis.org

5, 3, 5, 5, 3, 5, 3, 5, 2, 2, 4, 4, 4, 4, 3, 3, 3, 7, 7, 7, 4, 7, 4, 7, 7, 7, 4, 4, 3, 3, 3, 3, 3, 3, 5, 5, 4, 4, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 4, 6, 4, 2, 6, 6, 4, 2, 4, 6, 6, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 5, 9, 9, 9, 5, 5

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..25468
Index entries for the Kaprekar map

Cf. A165090, A165097, A165096, A165100, A165102, A165109.

In other bases: Empty (base 2), A165001 (base 3), A165020 (base 4), A165040 (base 5), A165059 (base 6), A165079 (base 7), A165118 (base 9), A164715 (base 10).

A165102 Length of cycle mentioned in A165101.

Original entry on oeis.org

5, 3, 2, 4, 3, 7, 4, 3, 3, 5, 5, 4, 3, 3, 3, 3, 6, 4, 2, 3, 3, 3, 3, 4, 2, 3, 3, 3, 5, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..8446
Index entries for the Kaprekar map

Cf. A165090, A165101, A165096, A165098, A165100, A165109.

In other bases: Empty (base 2), A165005 (base 3), A165024 (base 4), A165044 (base 5), A165063 (base 6), A165083 (base 7), A165122 (base 9), A164721 (base 10).

cp's OEIS Frontend

A165099 Consider the base-8 Kaprekar map n->K(n) defined in A165090. Sequence gives least elements of each cycle, including fixed points.

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A164719 Length of cycle mentioned in A164718.

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A165003 Length of cycle mentioned in A165002.

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A165022 Length of cycle mentioned in A165021.

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A165042 Length of cycle mentioned in A165041.

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A165061 Length of cycle mentioned in A165060.

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A165081 Length of cycle mentioned in A165080.

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A165096 Length of cycle mentioned in A165095.

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A165098 Length of cycle mentioned in A165097.

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A165102 Length of cycle mentioned in A165101.

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