A165062 -id:A165062 - cp's OEIS frontend

A165063 Length of cycle mentioned in A165062.

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

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..20656
Index entries for the Kaprekar map

Cf. A165051, A165062, A165057, A165059, A165061, A165070.

In other bases: Empty (base 2), A165005 (base 3), A165024 (base 4), A165044 (base 5), A165083 (base 7), A165102 (base 8), A165122 (base 9), A164721 (base 10).

A165056 Consider the base-6 Kaprekar map n->K(n) defined in A165051. Sequence gives numbers belonging to cycles, including fixed points.

Original entry on oeis.org

0, 105, 430, 675, 705, 860, 890, 920, 4305, 5180, 5600, 16840, 27195, 33860, 35510, 42745, 42925, 218960, 259105, 895275, 996315, 1174130, 1221860, 1275170, 1276250, 1282910, 1285070, 1338380, 1548445, 1563925, 1601755, 1657225

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 6: 0, 253, 1554, 3043, 3133, 3552, 4042, 4132, 31533, 35552.

Joseph Myers, Table of n, a(n) for n=1..43711
Index entries for the Kaprekar map

Union of A165055 and A165058. Cf. A165051, A165057, A165060, A165062, A165069, A165065.

In other bases: A163205 (base 2), A164998 (base 3), A165017 (base 4), A165037 (base 5), A165076 (base 7), A165095 (base 8), A165115 (base 9), A164716 (base 10).

A164720 Consider the Kaprekar map n->K(n) defined in A151949. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

53955, 61974, 62964, 420876, 7509843, 43208766, 64308654, 753098643, 4332087666, 6431088654, 6433086654, 6543086544, 9751088421, 76320987633, 86420987532, 433320876666, 643110888654, 643310886654, 643330866654

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..9501
Index entries for the Kaprekar map

Cf. A151949, A164721, A099009, A099010, A164716, A164718, A151965.

In other bases: Empty (base 2), A165004 (base 3), A165023 (base 4), A165043 (base 5), A165062 (base 6), A165082 (base 7), A165101 (base 8), A165121 (base 9). [From Joseph Myers, Sep 05 2009]

A165058 Consider the base-6 Kaprekar map n->K(n) defined in A165051. Sequence gives numbers belonging to cycles of length greater than 1.

Original entry on oeis.org

430, 675, 705, 860, 890, 920, 4305, 5180, 16840, 35510, 42745, 218960, 259105, 895275, 996315, 1174130, 1221860, 1276250, 1282910, 1285070, 1338380, 1548445, 1563925, 1601755, 7892360, 9392845, 44002820, 46288670, 55760125, 56412805

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 6: 1554, 3043, 3133, 3552, 4042, 4132, 31533, 35552, 205544, 432222.

Joseph Myers, Table of n, a(n) for n=1..41322
Index entries for the Kaprekar map

Cf. A165051, A165059, A165055, A165056, A165060, A165062, A165069.

In other bases: Empty (base 2), A165000 (base 3), A165019 (base 4), A165039 (base 5), A165078 (base 7), A165097 (base 8), A165117 (base 9), A099010 (base 10).

A165004 Consider the base-3 Kaprekar map n->K(n) defined in A164993. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

32, 320, 1696, 15304, 18208, 26240, 137776, 164008, 172720, 433012, 1240024, 1476208, 1554904, 1581040, 4487680, 11160256, 13286008, 13994560, 14230648, 14309056, 35075092, 42160852, 100442344, 106819600, 119574208, 125951464

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 3: 1012, 102212, 2022211, 202222211, 220222101, 1022222212, 20222222211, 22022222101, 22202221001, 210222222111.

Joseph Myers, Table of n, a(n) for n=1..20072
Index entries for the Kaprekar map

Cf. A164993, A165005, A164997, A164998, A165002, A165000, A165010.

In other bases: Empty (base 2), A165023 (base 4), A165043 (base 5), A165062 (base 6), A165082 (base 7), A165101 (base 8), A165121 (base 9), A164720 (base 10).

A165023 Consider the base-4 Kaprekar map n->K(n) defined in A165012. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

126, 570, 41958, 2788950, 178846038, 11451491670, 732979762518, 46912048616790, 3002392592864598, 192153469566932310, 12297827549946664278, 787061051157936166230, 50371908681484475913558

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 4: 1332, 20322, 22033212, 22220321112, 22222033211112, 22222203332111112, 22222220333321111112, 22222222033333211111112, 22222222203333332111111112, 22222222220333333321111111112.

Joseph Myers, Table of n, a(n) for n=1..67
Index entries for the Kaprekar map

Cf. A165012, A165024, A165016, A165017, A165021, A165019, A165030.

In other bases: Empty (base 2), A165004 (base 3), A165043 (base 5), A165062 (base 6), A165082 (base 7), A165101 (base 8), A165121 (base 9), A164720 (base 10).

A165043 Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

48, 1992, 7488, 53712, 249992, 6249992, 45781056, 170312312, 1144531056, 1205467776, 4514058432, 4576557032, 22460937432, 28613281056, 28671874056, 30136717776, 30441401376, 106445312312, 112304687432, 715332031056

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 5: 143, 30432, 214423, 3204322, 30444432, 3044444432, 43204443211, 322044443222, 4320444443211, 4432044432101.

Joseph Myers, Table of n, a(n) for n=1..15384
Index entries for the Kaprekar map

Cf. A165032, A165044, A165036, A165037, A165041, A165039, A165049.

In other bases: Empty (base 2), A165004 (base 3), A165023 (base 4), A165062 (base 6), A165082 (base 7), A165101 (base 8), A165121 (base 9), A164720 (base 10).

A165060 Consider the base-6 Kaprekar map n->K(n) defined in A165051. Sequence gives least elements of each cycle, including fixed points.

Original entry on oeis.org

0, 105, 430, 4305, 5600, 16840, 27195, 33860, 42925, 218960, 895275, 1221860, 1275170, 1548445, 1657225, 6018495, 7892360, 44002820, 45962330, 47681900, 55760125, 56319925, 59679145, 60331825, 277695950, 284180120, 348285175

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 6: 0, 253, 1554, 31533, 41532, 205544, 325523, 420432, 530421, 4405412.

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

Union of A165055 and A165062. Cf. A165051, A165061, A165056, A165058, A165069, A165064.

In other bases: A163205 (base 2), A165002 (base 3), A165021 (base 4), A165041 (base 5), A165080 (base 7), A165099 (base 8), A165119 (base 9), A164718 (base 10).

A165082 Consider the base-7 Kaprekar map n->K(n) defined in A165071. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

144, 1068, 9936, 55500, 640992, 3562968, 31412208, 220709400, 227429400, 228238488, 11150046252, 11432420652, 75796404672, 419850417612, 546394287000, 3939440152944, 26773614188652, 26884299308652

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 7: 264, 3054, 40653, 320544, 5306532, 42166443, 530666532, 5316666432, 5431055322, 5440665222.

Joseph Myers, Table of n, a(n) for n=1..8989
Index entries for the Kaprekar map

Cf. A165071, A165083, A165075, A165076, A165080, A165078, A165088.

In other bases: Empty (base 2), A165004 (base 3), A165023 (base 4), A165043 (base 5), A165062 (base 6), A165101 (base 8), A165121 (base 9), A164720 (base 10).

A165101 Consider the base-8 Kaprekar map n->K(n) defined in A165090. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

1022, 1589, 17892, 21483, 102837, 1445787, 1707930, 6589877, 13667738, 93093147, 110132442, 111443346, 421817781, 874802586, 878996762, 1029991697, 7034104602, 7168322322, 7302540042, 26996862389, 55987891610, 56256326938

Offset: 1

Joseph Myers, Sep 04 2009

Initial terms in base 8: 1776, 3065, 42744, 51753, 310665, 5407633, 6407632, 31106665, 64106632, 543076433.

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

Cf. A165090, A165102, A165094, A165095, A165099, A165097, A165108.

In other bases: Empty (base 2), A165004 (base 3), A165023 (base 4), A165043 (base 5), A165062 (base 6), A165082 (base 7), A165121 (base 9), A164720 (base 10).

cp's OEIS Frontend

A165063 Length of cycle mentioned in A165062.

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A165056 Consider the base-6 Kaprekar map n->K(n) defined in A165051. Sequence gives numbers belonging to cycles, including fixed points.

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A164720 Consider the Kaprekar map n->K(n) defined in A151949. Sequence gives least elements of each cycle of length > 1.

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A165058 Consider the base-6 Kaprekar map n->K(n) defined in A165051. Sequence gives numbers belonging to cycles of length greater than 1.

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A165004 Consider the base-3 Kaprekar map n->K(n) defined in A164993. Sequence gives least elements of each cycle of length > 1.

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A165023 Consider the base-4 Kaprekar map n->K(n) defined in A165012. Sequence gives least elements of each cycle of length > 1.

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A165043 Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives least elements of each cycle of length > 1.

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A165060 Consider the base-6 Kaprekar map n->K(n) defined in A165051. Sequence gives least elements of each cycle, including fixed points.

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A165082 Consider the base-7 Kaprekar map n->K(n) defined in A165071. Sequence gives least elements of each cycle of length > 1.

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A165101 Consider the base-8 Kaprekar map n->K(n) defined in A165090. Sequence gives least elements of each cycle of length > 1.

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