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

A165017 Consider the base-4 Kaprekar map n->K(n) defined in A165012. Sequence gives numbers belonging to cycles, including fixed points.

Original entry on oeis.org

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
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

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).

A165016 List of fixed points of the base-4 Kaprekar map A165012.

Original entry on oeis.org

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
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

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).

A165019 Consider the base-4 Kaprekar map n->K(n) defined in A165012. Sequence gives numbers belonging to cycles of length greater than 1.

Original entry on oeis.org

126, 138, 570, 765, 41958, 42966, 57333, 2788950, 3489705, 3833685, 178846038, 240385701, 245890389, 11451491670, 15657335445, 15745414485, 732979762518, 1006431627861, 1007840908629, 46912048616790, 64481417734485
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 4: 1332, 2022, 20322, 23331, 22033212, 22133112, 31333311, 22220321112, 31103332221, 32213331111.

Links

Crossrefs

Cf. A165012, A165020, A165016, A165017, A165021, A165023, A165030.
In other bases: Empty (base 2), A165000 (base 3), A165039 (base 5), A165058 (base 6), A165078 (base 7), A165097 (base 8), A165117 (base 9), A099010 (base 10).

A165021 Consider the base-4 Kaprekar map n->K(n) defined in A165012. Sequence gives least elements of each cycle, including fixed points.

Original entry on oeis.org

0, 30, 126, 201, 570, 2550, 3369, 3873, 14565, 41958, 54441, 62625, 64641, 171990, 234405, 254865, 873129, 954261, 1004193, 1036929, 1044993, 2788950, 3755685, 4083345, 4165185, 11140950, 13978281, 15285909, 16075425, 16399953, 16599681
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

Crossrefs

Union of A165016 and A165023. Cf. A165012, A165022, A165017, A165019, A165030, A165025.
In other bases: A163205 (base 2), A165002 (base 3), A165041 (base 5), A165060 (base 6), A165080 (base 7), A165099 (base 8), A165119 (base 9), A164718 (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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

Crossrefs

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).

A165025 Number of cycles of n-digit numbers (including fixed points) under the base-4 Kaprekar map A165012.

Original entry on oeis.org

1, 0, 1, 2, 1, 3, 1, 4, 3, 5, 4, 8, 5, 10, 8, 12, 10, 16, 12, 19, 16, 22, 19, 27, 22, 31, 27, 35, 31, 41, 35, 46, 41, 51, 46, 58, 51, 64, 58, 70, 64, 78, 70, 85, 78, 92, 85, 101, 92, 109, 101, 117, 109, 127, 117, 136, 127, 145, 136, 156, 145, 166, 156, 176, 166, 188, 176
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165012, A165017, A165026, A165027.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165006 (base 3), A165045 (base 5), A165064 (base 6), A165084 (base 7), A165103 (base 8), A165123 (base 9), A164731 (base 10).

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: x*(1 - x^2 + x^3 - 2*x^6 + 3*x^8 - x^10) / ((1 - x)^3*(1 + x)^2*(1 + x + x^2)).
a(n) = 2*a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) + a(n-7) for n>7.
(End)

A165026 Number of n-digit numbers in a cycle (including fixed points) under the base-4 Kaprekar map A165012.

Original entry on oeis.org

1, 0, 1, 3, 2, 3, 1, 6, 3, 5, 6, 8, 5, 12, 8, 12, 12, 16, 12, 21, 16, 22, 21, 27, 22, 33, 27, 35, 33, 41, 35, 48, 41, 51, 48, 58, 51, 66, 58, 70, 66, 78, 70, 87, 78, 92, 87, 101, 92, 111, 101, 117, 111, 127, 117, 138, 127, 145, 138, 156, 145, 168, 156, 176, 168, 188, 176
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165012, A165017, A165025, A165027.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165007 (base 3), A165046 (base 5), A165065 (base 6), A165085 (base 7), A165104 (base 8), A165124 (base 9), A164732 (base 10).

A165029 a(n) = smallest number that leads to a new cycle under the base-4 Kaprekar map of A165012.

Original entry on oeis.org

0, 18, 65, 66, 257, 1025, 1039, 1050, 4097, 16385, 16386, 16399, 16447, 65537, 65551, 65898, 262145, 262146, 262207, 262239, 262399, 1048577, 1048578, 1048591, 1048639, 4194305, 4194310, 4194319, 4194399, 4194559, 4194687, 4195327
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 4: 0, 102, 1001, 1002, 10001, 100001, 100033, 100122, 1000001, 10000001.

Links

Crossrefs

Cf. A165012, A165017, A165030, A165031.
In other bases: A164887 (base 2), A165009 (base 3), A165048 (base 5), A165068 (base 6), A165087 (base 7), A165107 (base 8), A165127 (base 9), A151964 (base 10).

A165014 Length of preperiodic part of trajectory of n under iteration of the base-4 Kaprekar map in A165012.

Original entry on oeis.org

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165012, A165015.
In other bases: A164885 (base 2), A164995 (base 3), A165034 (base 5), A165053 (base 6), A165073 (base 7), A165092 (base 8), A165112 (base 9), A151962 (base 10).

A165015 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-4 Kaprekar map in A165012.

Original entry on oeis.org

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165012, A165014.
In other bases: A164886 (base 2), A164996 (base 3), A165035 (base 5), A165054 (base 6), A165074 (base 7), A165093 (base 8), A165113 (base 9), A151963 (base 10).
Showing 1-10 of 30 results. Next

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