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

A165095 Consider the base-8 Kaprekar map n->K(n) defined in A165090. Sequence gives numbers belonging to cycles, including fixed points.

Original entry on oeis.org

0, 21, 252, 1022, 1589, 2044, 2212, 2723, 3122, 3178, 3290, 17892, 20475, 21483, 21987, 25578, 26586, 102837, 147420, 177443, 213402, 217938, 1445787, 1449819, 1646442, 1707930, 1711962, 1715994, 1740690, 1752786, 1777482, 1941345
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 8: 0, 25, 374, 1776, 3065, 3774, 4244, 5243, 6062, 6152.

Links

Crossrefs

Union of A165094 and A165097. Cf. A165090, A165096, A165099, A165101, A165108, A165104.
In other bases: A163205 (base 2), A164998 (base 3), A165017 (base 4), A165037 (base 5), A165056 (base 6), A165076 (base 7), A165115 (base 9), A164716 (base 10).

A165094 List of fixed points of the base-8 Kaprekar map A165090.

Original entry on oeis.org

0, 21, 252, 147420, 213402, 1711962, 16092433, 76545756, 1068263553, 39258683100, 57497839826, 58573445322, 68675650561, 3680015145170, 3749808363210, 4238480197777, 4397695901697, 20104741893852
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 8: 0, 25, 374, 437734, 640632, 6417532, 75306421, 443777334, 7753064201, 444377773334.

Links

Crossrefs

Cf. A165090, A165095, A165097, A165105.
In other bases: A163205 (base 2), A164997 (base 3), A165016 (base 4), A165036 (base 5), A165055 (base 6), A165075 (base 7), A165114 (base 9), A099009 (base 10).

A165097 Consider the base-8 Kaprekar map n->K(n) defined in A165090. Sequence gives numbers belonging to cycles of length greater than 1.

Original entry on oeis.org

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
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

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).

A165099 Consider the base-8 Kaprekar map n->K(n) defined in A165090. Sequence gives least elements of each cycle, including fixed points.

Original entry on oeis.org

0, 21, 252, 1022, 1589, 17892, 21483, 102837, 147420, 213402, 1445787, 1707930, 1711962, 6589877, 13667738, 16092433, 76545756, 93093147, 110132442, 111443346, 421817781, 874802586, 878996762, 1029991697, 1068263553
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

Crossrefs

Union of A165094 and A165101. Cf. A165090, A165100, A165095, A165097, A165108, A165103.
In other bases: A163205 (base 2), A165002 (base 3), A165021 (base 4), A165041 (base 5), A165060 (base 6), A165080 (base 7), A165119 (base 9), A164718 (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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

Crossrefs

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).

A165103 Number of cycles of n-digit numbers (including fixed points) under the base-8 Kaprekar map A165090.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 3, 13, 2, 16, 3, 21, 5, 34, 5, 45, 12, 62, 13, 82, 22, 104, 35, 137, 45, 170, 61, 215, 82, 264, 111, 323, 139, 389, 179, 466, 223, 564, 275, 657, 338, 774, 410, 905, 498, 1048, 587, 1212, 696, 1392, 818, 1598, 958, 1811, 1110, 2058, 1281
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165090, A165095, A165104, A165105.
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), A165123 (base 9), A164731 (base 10).

A165104 Number of n-digit numbers in a cycle (including fixed points) under the base-8 Kaprekar map A165090.

Original entry on oeis.org

1, 1, 1, 8, 6, 5, 12, 7, 15, 13, 12, 31, 14, 40, 14, 59, 12, 96, 11, 137, 24, 184, 35, 234, 64, 300, 102, 391, 134, 494, 175, 630, 232, 782, 311, 954, 402, 1147, 521, 1374, 659, 1649, 814, 1943, 992, 2294, 1203, 2687, 1454, 3117, 1731, 3597, 2060, 4130, 2430, 4734
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165090, A165095, A165103, A165105.
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), A165124 (base 9), A164732 (base 10).

A165107 a(n) = smallest number that leads to a new cycle under the base-8 Kaprekar map of A165090.

Original entry on oeis.org

0, 12, 66, 513, 514, 4097, 4124, 32769, 32779, 32868, 262145, 262148, 262291, 2097153, 2097155, 2097227, 16777217, 16777218, 16777219, 16782116, 134217729, 134217731, 134217739, 134218315, 134219007, 1073741825, 1073741826
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 8: 0, 14, 102, 1001, 1002, 10001, 10034, 100001, 100013, 100144.

Links

Crossrefs

Cf. A165090, A165095, A165108, A165109.
In other bases: A164887 (base 2), A165009 (base 3), A165029 (base 4), A165048 (base 5), A165068 (base 6), A165087 (base 7), A165127 (base 9), A151964 (base 10).

A165092 Length of preperiodic part of trajectory of n under iteration of the base-8 Kaprekar map in A165090.

Original entry on oeis.org

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165090, A165093.
In other bases: A164885 (base 2), A164995 (base 3), A165014 (base 4), A165034 (base 5), A165053 (base 6), A165073 (base 7), A165112 (base 9), A151962 (base 10).

A165093 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-8 Kaprekar map in A165090.

Original entry on oeis.org

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165090, A165092.
In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165035 (base 5), A165054 (base 6), A165074 (base 7), A165113 (base 9), A151963 (base 10).
Showing 1-10 of 30 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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