A165109 -id:A165109 - cp's OEIS frontend

A165100 Length of cycle mentioned in A165099.

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

Offset: 1

Joseph Myers, Sep 04 2009

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

Cf. A165090, A165099, A165096, A165098, A165102, A165109.

In other bases: A000012 (base 2), A165003 (base 3), A165022 (base 4), A165042 (base 5), A165061 (base 6), A165081 (base 7), A165120 (base 9), A164719 (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).

A165107 a(n) = smallest number that leads to a new cycle under the base-8 Kaprekar map of A165090.

Original entry on oeis.org

0, 12, 66, 513, 514, 4097, 4124, 32769, 32779, 32868, 262145, 262148, 262291, 2097153, 2097155, 2097227, 16777217, 16777218, 16777219, 16782116, 134217729, 134217731, 134217739, 134218315, 134219007, 1073741825, 1073741826

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 8: 0, 14, 102, 1001, 1002, 10001, 10034, 100001, 100013, 100144.

Joseph Myers, Table of n, a(n) for n=1..8775
Index entries for the Kaprekar map

Cf. A165090, A165095, A165108, A165109.

In other bases: A164887 (base 2), A165009 (base 3), A165029 (base 4), A165048 (base 5), A165068 (base 6), A165087 (base 7), A165127 (base 9), A151964 (base 10).

cp's OEIS Frontend

A165100 Length of cycle mentioned in A165099.

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A165102 Length of cycle mentioned in A165101.

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A165107 a(n) = smallest number that leads to a new cycle under the base-8 Kaprekar map of A165090.

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