A165049 -id:A165049

A165037

Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives numbers belonging to cycles, including fixed points.

+10
19

0, 8, 48, 72, 392, 1992, 2232, 2616, 2856, 7488, 9992, 10712, 11432, 13736, 53712, 57432, 66216, 73056, 249992, 272312, 284832, 287432, 347336, 349936, 1831056, 6249992, 8687336, 8785936, 9236656, 45781056, 45874056, 46264656, 48217776

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

OFFSET

1,2

COMMENTS

Initial terms in base 5: 0, 13, 143, 242, 3032, 30432, 32412, 40431, 42411, 214423.

LINKS

Joseph Myers, Table of n, a(n) for n=1..36814

Index entries for the Kaprekar map

CROSSREFS

Union of A165036 and A165039. Cf. A165032, A165038, A165041, A165043, A165049, A165046.

In other bases: A163205 (base 2), A164998 (base 3), A165017 (base 4), 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

A165010

Smallest member of cycle corresponding to n-th term of A165009

+10
14

0, 32, 184, 320, 1696, 2008, 5332, 15304, 18208, 19144, 26240, 55360, 137776, 164008, 146488, 172720, 175528, 433012, 520372, 1240024, 1476208, 1554904, 1502344, 1581040, 1589464, 3975844, 4487680, 4749760, 11160256, 13286008

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

OFFSET

1,2

COMMENTS

Initial terms in base 3: 0, 1012, 20211, 102212, 2022211, 2202101, 21022111, 202222211, 220222101, 222021001.

LINKS

Joseph Myers, Table of n, a(n) for n=1..23340

Index entries for the Kaprekar map

CROSSREFS

Cf. A164993, A164998, A165009, A165011.

In other bases: A163205 (base 2), A165030 (base 4), A165049 (base 5), A165069 (base 6), A165088 (base 7), A165108 (base 8), A165128 (base 9), A151965 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165030

Smallest member of cycle corresponding to n-th term of A165029

+10
14

0, 30, 201, 126, 570, 3369, 3873, 2550, 14565, 41958, 54441, 62625, 64641, 234405, 254865, 171990, 873129, 954261, 1036929, 1004193, 1044993, 3755685, 2788950, 4083345, 4165185, 15285909, 13978281, 16075425, 16399953, 16730625, 16599681

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

OFFSET

1,2

COMMENTS

Initial terms in base 4: 0, 132, 3021, 1332, 20322, 310221, 330201, 213312, 3203211, 22033212.

LINKS

Joseph Myers, Table of n, a(n) for n=1..7165

Index entries for the Kaprekar map

CROSSREFS

Cf. A165012, A165017, A165029, A165031.

In other bases: A163205 (base 2), A165010 (base 3), A165049 (base 5), A165069 (base 6), A165088 (base 7), A165108 (base 8), A165128 (base 9), A151965 (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

A165050

Length of cycle corresponding to n-th term of A165048.

+10
14

1, 1, 2, 1, 4, 5, 4, 6, 1, 4, 3, 1, 8, 5, 3, 1, 4, 5, 6, 2, 4, 5, 3, 1, 4, 1, 5, 4, 4, 2, 2, 2, 6, 5, 3, 1, 5, 1, 4, 4, 4, 4, 3, 2, 4, 4, 2, 6, 5, 2, 3, 1, 3, 1, 9, 3, 9, 4, 4, 4, 2, 4, 4, 4, 2, 6, 5, 2, 3, 1, 5, 5, 3, 1, 6, 3, 2, 6, 6, 3, 9, 1, 9, 4, 4, 3, 4, 2, 4, 4, 4, 2, 6, 5, 2, 3, 1, 11, 5, 3, 1, 11, 11

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

OFFSET

1,3

LINKS

Joseph Myers, Table of n, a(n) for n=1..15716

Index entries for the Kaprekar map

CROSSREFS

Cf. A165032, A165037, A165048, A165049.

In other bases: A000012 (base 2), A165011 (base 3), A165031 (base 4), A165070 (base 6), A165089 (base 7), A165109 (base 8), A165129 (base 9), A151966 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165069

Smallest member of cycle corresponding to n-th term of A165068

+10
14

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

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

OFFSET

1,2

COMMENTS

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

LINKS

Joseph Myers, Table of n, a(n) for n=1..23045

Index entries for the Kaprekar map

CROSSREFS

Cf. A165051, A165056, A165068, A165070.

In other bases: A163205 (base 2), A165010 (base 3), A165030 (base 4), A165049 (base 5), A165088 (base 7), A165108 (base 8), A165128 (base 9), A151965 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165088

Smallest member of cycle corresponding to n-th term of A165087

+10
14

0, 144, 1068, 9936, 55500, 640992, 3562968, 31412208, 228238488, 227429400, 220709400, 1922263344, 11432420652, 11150046252, 75796404672, 94197649008, 96503566608, 546394287000, 419850417612, 4615731883344, 3939440152944

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

OFFSET

1,2

COMMENTS

Initial terms in base 7: 0, 264, 3054, 40653, 320544, 5306532, 42166443, 530666532, 5440665222, 5431055322.

LINKS

Joseph Myers, Table of n, a(n) for n=1..13070

Index entries for the Kaprekar map

CROSSREFS

Cf. A165071, A165076, A165087, A165089.

In other bases: A163205 (base 2), A165010 (base 3), A165030 (base 4), A165049 (base 5), A165069 (base 6), A165108 (base 8), A165128 (base 9), A151965 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165108

Smallest member of cycle corresponding to n-th term of A165107

+10
14

0, 21, 252, 1589, 1022, 21483, 17892, 213402, 102837, 147420, 1445787, 1707930, 1711962, 13667738, 16092433, 6589877, 110132442, 111443346, 93093147, 76545756, 878996762, 1029991697, 874802586, 421817781, 1068263553

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

OFFSET

1,2

COMMENTS

Initial terms in base 8: 0, 25, 374, 3065, 1776, 51753, 42744, 640632, 310665, 437734.

LINKS

Joseph Myers, Table of n, a(n) for n=1..8775

Index entries for the Kaprekar map

CROSSREFS

Cf. A165090, A165095, A165107, A165109.

In other bases: A163205 (base 2), A165010 (base 3), A165030 (base 4), A165049 (base 5), A165069 (base 6), A165088 (base 7), A165128 (base 9), A151965 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165128

Smallest member of cycle corresponding to n-th term of A165127

+10
14

0, 16, 320, 2256, 3712, 34960, 41520, 183696, 3496800, 31596672, 31531872, 278474880, 326952560, 2066242576, 2516902752, 2598744000, 26531651360, 23087388720, 167365651216, 203869268832, 211282856832, 2184410558000

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

OFFSET

1,2

COMMENTS

Initial terms in base 9: 0, 17, 385, 3076, 5074, 52854, 62853, 308876, 6518633, 65407433.

LINKS

Joseph Myers, Table of n, a(n) for n=1..1560

Index entries for the Kaprekar map

CROSSREFS

Cf. A165110, A165115, A165127, A165129.

In other bases: A163205 (base 2), A165010 (base 3), A165030 (base 4), A165049 (base 5), A165069 (base 6), A165088 (base 7), A165108 (base 8), A151965 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved

A165041

Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives least elements of each cycle, including fixed points.

+10
13

0, 8, 48, 392, 1992, 7488, 53712, 249992, 1831056, 6249992, 45781056, 48217776, 170312312, 1144531056, 1205467776, 1217651376, 4514058432, 4576557032, 22460937432, 28613281056, 28671874056, 30136717776, 30441401376

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

OFFSET

1,2

COMMENTS

Initial terms in base 5: 0, 13, 143, 3032, 30432, 214423, 3204322, 30444432, 432043211, 3044444432.

LINKS

Joseph Myers, Table of n, a(n) for n=1..15716

Anthony Kay and Katrina Downes-Ward, Fixed Points and Cycles of the Kaprekar Transformation: 1. Odd Bases, Journal of Integer Sequences, Vol. 25 (2022), Article 22.6.7.

Index entries for the Kaprekar map

CROSSREFS

Union of A165036 and A165043. Cf. A165032, A165042, A165037, A165039, A165049, A165045.

In other bases: A163205 (base 2), A165002 (base 3), A165021 (base 4), A165060 (base 6), A165080 (base 7), A165099 (base 8), A165119 (base 9), A164718 (base 10).

KEYWORD

base,nonn

AUTHOR

Joseph Myers, Sep 04 2009

STATUS

approved