A164716 -id:A164716 - cp's OEIS frontend

A164731 Number of cycles of n-digit numbers (including fixed points) under the Kaprekar map A151949.

1, 0, 1, 1, 3, 3, 1, 4, 3, 8, 3, 16, 5, 27, 8, 46, 9, 73, 11, 110, 16, 162, 25, 231, 37, 318, 58, 429, 88, 572, 132, 747, 192, 963, 269, 1229, 372, 1551, 500, 1939, 662, 2401, 864, 2948, 1115, 3586, 1421, 4330, 1792, 5194, 2240, 6191, 2764, 7338, 3382, 8650, 4105

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..70
H. Hanslik, E. Hetmaniok, I. Sobstyl, et al., Orbits of the Kaprekar's transformations-some introductory facts, Zeszyty Naukowe Politechniki Śląskiej, Seria: Matematyka Stosowana z. 5, Nr kol. 1945; 2015.
Index entries for the Kaprekar map

Cf. A151949, A164716, A164732, A164733, A164734, A164735, A164736.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165006 (base 3), A165025 (base 4), A165045 (base 5), A165064 (base 6), A165084 (base 7), A165103 (base 8), A165123 (base 9). [Joseph Myers, Sep 05 2009]

A164732 Number of n-digit numbers in a cycle (including fixed points) under the Kaprekar map A151949.

Original entry on oeis.org

1, 0, 1, 1, 10, 9, 8, 12, 16, 22, 14, 42, 18, 73, 29, 125, 34, 199, 38, 308, 49, 462, 71, 665, 105, 920, 161, 1243, 249, 1658, 379, 2170, 555, 2806, 780, 3587, 1075, 4539, 1449, 5689, 1922, 7059, 2516, 8677, 3252, 10566, 4156, 12774, 5255, 15337, 6578, 18300

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..70
H. Hanslik, E. Hetmaniok, I. Sobstyl, et al., Orbits of the Kaprekar's transformations-some introductory facts, Zeszyty Naukowe Politechniki Śląskiej, Seria: Matematyka Stosowana z. 5, Nr kol. 1945; 2015.
Index entries for the Kaprekar map

Cf. A151949, A164716, A164731, A164733, A164734, A164735, A164736.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165007 (base 3), A165026 (base 4), A165046 (base 5), A165065 (base 6), A165085 (base 7), A165104 (base 8), A165124 (base 9). [Joseph Myers, Sep 05 2009]

A164723 Numbers belonging to cycles of length 2 under the Kaprekar map A151949.

Original entry on oeis.org

53955, 59994, 8733209876622, 9665429654331, 873332098766622, 966543296654331, 8764421997755322, 8765431997654322, 87333320987666622, 96654332966654331, 8733333209876666622, 9665433329666654331

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..1146
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A099010, A164716, A164725, A164727, A164729, A164724.

A164725 Numbers belonging to cycles of length 3 under the Kaprekar map A151949.

Original entry on oeis.org

64308654, 83208762, 86526432, 6431088654, 6433086654, 6543086544, 8321088762, 8332087662, 8653266432, 8655264432, 8732087622, 8765264322, 9751088421, 9755084421, 9775084221, 643110888654, 643310886654, 643330866654

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..27849
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A099010, A164716, A164723, A164727, A164729, A164726.

A164727 Numbers belonging to cycles of length 5 under the Kaprekar map A151949.

Original entry on oeis.org

86420987532, 86541975432, 87641975322, 88431976512, 96641975331, 8643209876532, 8654209875432, 8654319765432, 8764209875322, 8764319765322, 8765419754322, 8843209876512, 8843319766512, 8854319765412, 8874319765212

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..14510
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A099010, A164716, A164723, A164725, A164729, A164728.

A164729 Numbers belonging to cycles of length 7 under the Kaprekar map A151949.

Original entry on oeis.org

420876, 642654, 750843, 840852, 851742, 860832, 862632, 43208766, 64326654, 75308643, 84308652, 85317642, 86308632, 86326632, 4332087666, 6433266654, 7533086643, 8433086652, 8533176642, 8633086632, 8633266632, 433320876666

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..476
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A099010, A164716, A164723, A164725, A164727, A164730.

cp's OEIS Frontend

A164731 Number of cycles of n-digit numbers (including fixed points) under the Kaprekar map A151949.

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A164732 Number of n-digit numbers in a cycle (including fixed points) under the Kaprekar map A151949.

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A164723 Numbers belonging to cycles of length 2 under the Kaprekar map A151949.

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A164725 Numbers belonging to cycles of length 3 under the Kaprekar map A151949.

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A164727 Numbers belonging to cycles of length 5 under the Kaprekar map A151949.

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A164729 Numbers belonging to cycles of length 7 under the Kaprekar map A151949.

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