cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 30 results. Next

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

Crossrefs

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).

A165055 List of fixed points of the base-6 Kaprekar map A165051.

Original entry on oeis.org

0, 105, 5600, 27195, 33860, 42925, 1275170, 1657225, 6018495, 45962330, 47681900, 56319925, 60331825, 277695950, 348285175, 1305060855, 2151904825, 2175976225, 10363227560, 12973622725, 59994427550, 60063064790, 73115587525
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 6: 0, 253, 41532, 325523, 420432, 530421, 43155322, 55304201, 332555223, 4321044322.

Links

Crossrefs

Cf. A165051, A165056, A165058, A165066.
In other bases: A163205 (base 2), A164997 (base 3), A165016 (base 4), A165036 (base 5), A165075 (base 7), A165094 (base 8), A165114 (base 9), A099009 (base 10).

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

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).

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

Crossrefs

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).

A165062 Consider the base-6 Kaprekar map n->K(n) defined in A165051. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

430, 4305, 16840, 218960, 895275, 1221860, 1548445, 7892360, 44002820, 55760125, 59679145, 284180120, 1584195140, 1654738970, 2007458365, 2027613685, 2148546025, 2172060145, 10230811640, 12538603735, 57031585220, 59571164570
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 6: 1554, 31533, 205544, 4405412, 31104443, 42104432, 53104421, 441054412, 4211044432, 5311044421.

Links

Crossrefs

Cf. A165051, A165063, A165055, A165056, A165060, A165058, A165069.
In other bases: Empty (base 2), A165004 (base 3), A165023 (base 4), A165043 (base 5), A165082 (base 7), A165101 (base 8), A165121 (base 9), A164720 (base 10).

A165064 Number of cycles of n-digit numbers (including fixed points) under the base-6 Kaprekar map A165051.

Original entry on oeis.org

1, 0, 1, 1, 2, 4, 1, 5, 2, 7, 3, 9, 4, 13, 7, 17, 8, 24, 11, 30, 16, 37, 21, 46, 27, 57, 34, 68, 42, 83, 52, 96, 64, 113, 77, 132, 90, 153, 107, 175, 125, 200, 145, 226, 168, 256, 191, 288, 217, 323, 247, 358, 278, 399, 312, 441, 348, 487, 387, 536, 429, 587, 475, 641
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165051, A165056, A165065, A165066.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165006 (base 3), A165025 (base 4), A165045 (base 5), A165084 (base 7), A165103 (base 8), A165123 (base 9), A164731 (base 10).

Formula

G.f.: x*(1 + x + 2*x^5 - 2*x^7 - 3*x^8 - 3*x^9 - x^10 + 2*x^11 + 4*x^12 + 4*x^13 + 4*x^14 + x^15 - 3*x^16 - 3*x^17 - 2*x^18 - x^19 + x^21 + x^22) / ((1 - x)^4*(1 + x)^3*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) (conjectured). - Colin Barker, Jun 01 2017

A165065 Number of n-digit numbers in a cycle (including fixed points) under the base-6 Kaprekar map A165051.

Original entry on oeis.org

1, 0, 1, 6, 3, 6, 2, 13, 3, 10, 4, 15, 6, 21, 10, 29, 13, 40, 18, 52, 26, 65, 35, 82, 46, 101, 59, 123, 74, 149, 92, 176, 114, 207, 138, 243, 164, 282, 195, 325, 229, 372, 267, 423, 310, 479, 355, 541, 405, 607, 461, 677, 521, 754, 586, 836, 656, 924, 731, 1019, 812
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165051, A165056, A165064, A165066.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165007 (base 3), A165026 (base 4), A165046 (base 5), A165085 (base 7), A165104 (base 8), A165124 (base 9), A164732 (base 10).

A165068 a(n) = smallest number that leads to a new cycle under the base-6 Kaprekar map of A165051.

Original entry on oeis.org

0, 38, 217, 1297, 1311, 7777, 7779, 7790, 7833, 46657, 279937, 279938, 279986, 280043, 280238, 1679617, 1681257, 10077697, 10077698, 10077710, 10077803, 10077962, 10078343, 10079524, 60466177, 60466179, 60475766, 362797057
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 6: 0, 102, 1001, 10001, 10023, 100001, 100003, 100022, 100133, 1000001.

Links

Crossrefs

Cf. A165051, A165056, A165069, A165070.
In other bases: A164887 (base 2), A165009 (base 3), A165029 (base 4), A165048 (base 5), A165087 (base 7), A165107 (base 8), A165127 (base 9), A151964 (base 10).

A165053 Length of preperiodic part of trajectory of n under iteration of the base-6 Kaprekar map in A165051.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 2, 1, 2, 4, 3, 3, 4, 2, 1, 2, 4, 3, 3, 4, 2, 1, 2, 4, 3, 3, 4, 2, 1, 2, 4, 3, 3, 4, 2, 1, 2, 2, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 3, 2, 2, 3, 1, 2, 1, 3, 3, 3, 1, 2, 2, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 2, 3, 3, 3, 1, 2, 3, 3, 2, 2, 3, 1, 2, 3, 2, 1, 2, 3, 1, 1, 3, 2, 2, 3, 1, 2, 1, 3, 3, 3, 1, 3, 2, 1
Offset: 0

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165051, A165054.
In other bases: A164885 (base 2), A164995 (base 3), A165014 (base 4), A165034 (base 5), A165073 (base 7), A165092 (base 8), A165112 (base 9), A151962 (base 10).

A165054 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-6 Kaprekar map in A165051.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 3, 2, 3, 5, 4, 4, 5, 3, 2, 3, 5, 4, 4, 5, 3, 2, 3, 5, 4, 4, 5, 3, 2, 3, 5, 4, 4, 5, 3, 2, 3, 3, 4, 2, 3, 4, 3, 2, 3, 4, 2, 3, 4, 3, 3, 4, 2, 3, 2, 4, 4, 4, 2, 3, 3, 2, 2, 2, 2, 3, 4, 3, 3, 3, 3, 3, 4, 4, 4, 2, 3, 4, 4, 3, 3, 4, 2, 3, 4, 3, 2, 3, 4, 2, 2, 4, 3, 3, 4, 2, 3, 2, 4, 4, 4, 2, 4, 3, 2
Offset: 0

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165051, A165053.
In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165035 (base 5), A165074 (base 7), A165093 (base 8), A165113 (base 9), A151963 (base 10).
Showing 1-10 of 30 results. Next

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