A165019 -id:A165019

A165020

Length of cycle mentioned in A165019

+20
13

2, 2, 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, 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Joseph Myers, Table of n, a(n) for n=1..199

Index entries for the Kaprekar map

CROSSREFS

Cf. A165012, A165019, A165018, A165022, A165024, A165031.

In other bases: Empty (base 2), A165001 (base 3), A165040 (base 5), A165059 (base 6), A165079 (base 7), A165098 (base 8), A165118 (base 9), A164715 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A099010

Consider the Kaprekar map n->K(n) defined in A151949. Sequence gives numbers belonging to cycles of length greater than 1.

+10
20

53955, 59994, 61974, 62964, 63954, 71973, 74943, 75933, 82962, 83952, 420876, 642654, 750843, 840852, 851742, 860832, 862632, 7509843, 7519743, 7619733, 8429652, 8439552, 8649432, 8719722, 9529641, 43208766, 64308654, 64326654

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

86526432, 64308654, 83208762 form a cycle of length three and 86308632, 86326632, 64326654, 43208766, 85317642, 75308643, 84308652 form a cycle of length seven.

LINKS

Joseph Myers, Table of n, a(n) for n=1..28910 [From Joseph Myers, Aug 22 2009]

Eric Weisstein's World of Mathematics, Kaprekar Routine

Index entries for the Kaprekar map

EXAMPLE

53955 and 59994 form a cycle of length 2 and hence are terms: 53955 -> 95553 - 35559 = 59994 -> 99954 - 45999 = 53955.

CROSSREFS

Cf. A151949, A090429, A069746, A099009.

Cf. A164715 (corresponding cycle lengths) [From Joseph Myers, Aug 24 2009]

In other bases: Empty (base 2), A165000 (base 3), A165019 (base 4), A165039 (base 5), A165058 (base 6), A165078 (base 7), A165097 (base 8), A165117 (base 9). [From Joseph Myers, Sep 05 2009]

KEYWORD

nonn,base

AUTHOR

Klaus Brockhaus, Sep 22 2004

EXTENSIONS

Definition revised ny N. J. A. Sloane, Aug 18 2009

Extended by Joseph Myers, Aug 22 2009

STATUS

approved

A165017

Consider the base-4 Kaprekar map n->K(n) defined in A165012. Sequence gives numbers belonging to cycles, including fixed points.

+10
19

0, 30, 126, 138, 201, 570, 765, 2550, 3369, 3873, 14565, 41958, 42966, 54441, 57333, 62625, 64641, 171990, 234405, 254865, 873129, 954261, 1004193, 1036929, 1044993, 2788950, 3489705, 3755685, 3833685, 4083345, 4165185, 11140950, 13978281

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Initial terms in base 4: 0, 132, 1332, 2022, 3021, 20322, 23331, 213312, 310221, 330201.

LINKS

Joseph Myers, Table of n, a(n) for n=1..7217

Index entries for the Kaprekar map

CROSSREFS

Union of A165016 and A165019. Cf. A165012, A165018, A165021, A165023, A165030, A165026.

In other bases: A163205 (base 2), A164998 (base 3), A165037 (base 5), A165056 (base 6), A165076 (base 7), A165095 (base 8), A165115 (base 9), A164716 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165016

List of fixed points of the base-4 Kaprekar map A165012

+10
17

0, 30, 201, 2550, 3369, 3873, 14565, 54441, 62625, 64641, 171990, 234405, 254865, 873129, 954261, 1004193, 1036929, 1044993, 3755685, 4083345, 4165185, 11140950, 13978281, 15285909, 16075425, 16399953, 16599681, 16730625, 16762881

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Initial terms in base 4: 0, 132, 3021, 213312, 310221, 330201, 3203211, 31102221, 33102201, 33302001.

LINKS

Joseph Myers, Table of n, a(n) for n=1..7138

Index entries for the Kaprekar map

CROSSREFS

Cf. A165012, A165017, A165019, A165027.

In other bases: A163205 (base 2), A164997 (base 3), A165036 (base 5), A165055 (base 6), A165075 (base 7), A165094 (base 8), A165114 (base 9), A099009 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165000

Consider the base-3 Kaprekar map n->K(n) defined in A164993. Sequence gives numbers belonging to cycles of length greater than 1.

+10
14

32, 52, 320, 484, 580, 1696, 1768, 15304, 16024, 16240, 18208, 18424, 26240, 39364, 48100, 48964, 137776, 144328, 147136, 164008, 166168, 166816, 172720, 173368, 433012, 441652, 1240024, 1299064, 1318720, 1325200, 1327144, 1476208, 1495864

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Initial terms in base 3: 1012, 1221, 102212, 122221, 210111, 2022211, 2102111, 202222211, 210222111, 211021111.

LINKS

Joseph Myers, Table of n, a(n) for n=1..8276

Index entries for the Kaprekar map

CROSSREFS

Cf. A164993, A165001, A164997, A164998, A165002, A165004, A165010.

In other bases: Empty (base 2), A165019 (base 4), A165039 (base 5), A165058 (base 6), A165078 (base 7), A165097 (base 8), A165117 (base 9), A099010 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165039

Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives numbers belonging to cycles of length greater than 1

+10
14

48, 72, 1992, 2232, 2616, 2856, 7488, 9992, 10712, 11432, 13736, 53712, 57432, 66216, 73056, 249992, 272312, 284832, 287432, 347336, 349936, 6249992, 8687336, 8785936, 9236656, 45781056, 45874056, 46264656, 170312312, 178124832

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Initial terms in base 5: 143, 242, 30432, 32412, 40431, 42411, 214423, 304432, 320322, 331212.

LINKS

Joseph Myers, Table of n, a(n) for n=1..36656

Index entries for the Kaprekar map

CROSSREFS

Cf. A165032, A165040, A165036, A165037, A165041, A165043, A165049.

In other bases: Empty (base 2), A165000 (base 3), A165019 (base 4), A165058 (base 6), A165078 (base 7), A165097 (base 8), A165117 (base 9), A099010 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165058

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

+10
14

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Joseph Myers, Table of n, a(n) for n=1..41322

Index entries for the Kaprekar map

CROSSREFS

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).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165078

Consider the base-7 Kaprekar map n->K(n) defined in A165071. Sequence gives numbers belonging to cycles of length greater than 1

+10
14

144, 192, 1068, 1752, 1836, 9936, 10608, 13008, 13680, 15072, 55500, 72012, 77388, 89112, 91212, 91800, 640992, 643344, 660144, 674592, 760992, 780144, 3562968, 4605036, 4642668, 4772952, 5445336, 5464152, 31412208, 31680336, 32353344

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Initial terms in base 7: 264, 363, 3054, 5052, 5232, 40653, 42633, 52632, 54612, 61641.

LINKS

Joseph Myers, Table of n, a(n) for n=1..32041

Index entries for the Kaprekar map

CROSSREFS

Cf. A165071, A165079, A165075, A165076, A165080, A165082, A165088.

In other bases: Empty (base 2), A165000 (base 3), A165019 (base 4), A165039 (base 5), A165058 (base 6), A165097 (base 8), A165117 (base 9), A099010 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165097

Consider the base-8 Kaprekar map n->K(n) defined in A165090. Sequence gives numbers belonging to cycles of length greater than 1

+10
14

1022, 1589, 2044, 2212, 2723, 3122, 3178, 3290, 17892, 20475, 21483, 21987, 25578, 26586, 102837, 177443, 217938, 1445787, 1449819, 1646442, 1707930, 1715994, 1740690, 1752786, 1777482, 1941345, 1978137, 1982169, 6589877, 11381027

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Initial terms in base 8: 1776, 3065, 3774, 4244, 5243, 6062, 6152, 6332, 42744, 47773.

LINKS

Joseph Myers, Table of n, a(n) for n=1..25468

Index entries for the Kaprekar map

CROSSREFS

Cf. A165090, A165098, A165094, A165095, A165099, A165101, A165108.

In other bases: Empty (base 2), A165000 (base 3), A165019 (base 4), A165039 (base 5), A165058 (base 6), A165078 (base 7), A165117 (base 9), A099010 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165117

Consider the base-9 Kaprekar map n->K(n) defined in A165110. Sequence gives numbers belonging to cycles of length greater than 1

+10
14

16, 48, 320, 400, 2256, 3712, 3856, 5168, 5312, 5456, 34960, 40080, 42240, 49520, 55360, 183696, 250592, 308992, 322096, 323392, 388992, 419888, 440192, 446096, 448688, 454592, 505792, 511696, 512992, 3496800, 3916640, 31596672, 35193008

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Initial terms in base 9: 17, 53, 385, 484, 3076, 5074, 5254, 7072, 7252, 7432.

LINKS

Joseph Myers, Table of n, a(n) for n=1..7548

Index entries for the Kaprekar map

CROSSREFS

Cf. A165110, A165118, A165114, A165115, A165119, A165121, A165128.

In other bases: Empty (base 2), A165000 (base 3), A165019 (base 4), A165039 (base 5), A165058 (base 6), A165078 (base 7), A165097 (base 8), A099010 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved