A165031 -id:A165031 - cp's OEIS frontend

A165022 Length of cycle mentioned in A165021.

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).

A165024 Length of cycle mentioned in A165023.

Original entry on oeis.org

2, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Joseph Myers, Sep 04 2009

Index entries for the Kaprekar map

Cf. A165012, A165023, A165018, A165020, A165022, A165031.

In other bases: Empty (base 2), A165005 (base 3), A165044 (base 5), A165063 (base 6), A165083 (base 7), A165102 (base 8), A165122 (base 9), A164721 (base 10).

A165029 a(n) = smallest number that leads to a new cycle under the base-4 Kaprekar map of A165012.

Original entry on oeis.org

0, 18, 65, 66, 257, 1025, 1039, 1050, 4097, 16385, 16386, 16399, 16447, 65537, 65551, 65898, 262145, 262146, 262207, 262239, 262399, 1048577, 1048578, 1048591, 1048639, 4194305, 4194310, 4194319, 4194399, 4194559, 4194687, 4195327

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 4: 0, 102, 1001, 1002, 10001, 100001, 100033, 100122, 1000001, 10000001.

Joseph Myers, Table of n, a(n) for n=1..7165
Index entries for the Kaprekar map

Cf. A165012, A165017, A165030, A165031.

In other bases: A164887 (base 2), A165009 (base 3), A165048 (base 5), A165068 (base 6), A165087 (base 7), A165107 (base 8), A165127 (base 9), A151964 (base 10).

cp's OEIS Frontend

A165022 Length of cycle mentioned in A165021.

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A165024 Length of cycle mentioned in A165023.

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A165029 a(n) = smallest number that leads to a new cycle under the base-4 Kaprekar map of A165012.

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