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 29 results. Next

A165037 Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives numbers belonging to cycles, including fixed points.

Original entry on oeis.org

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
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

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).

A165036 List of fixed points of the base-5 Kaprekar map A165032.

Original entry on oeis.org

0, 8, 392, 1831056, 48217776, 1217651376, 30502319376, 144640604656, 762863159376, 3774960835776, 19073104859376, 95168749491376, 476835250859376, 2383192380269376, 11320075681132656, 11920919418359376
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 5: 0, 13, 3032, 432043211, 44320432101, 4443204321001, 444432043210001, 4332210443322111, 44444320432100001, 443322104433221101.

Links

Crossrefs

Cf. A165032, A165037, A165039, A008617.
In other bases: A163205 (base 2), A164997 (base 3), A165016 (base 4), A165055 (base 6), A165075 (base 7), A165094 (base 8), A165114 (base 9), A099009 (base 10).

A165039 Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives numbers belonging to cycles of length greater than 1.

Original entry on oeis.org

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
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

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).

A165041 Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives least elements of each cycle, including fixed points.

Original entry on oeis.org

0, 8, 48, 392, 1992, 7488, 53712, 249992, 1831056, 6249992, 45781056, 48217776, 170312312, 1144531056, 1205467776, 1217651376, 4514058432, 4576557032, 22460937432, 28613281056, 28671874056, 30136717776, 30441401376
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

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

Links

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).

A165043 Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

48, 1992, 7488, 53712, 249992, 6249992, 45781056, 170312312, 1144531056, 1205467776, 4514058432, 4576557032, 22460937432, 28613281056, 28671874056, 30136717776, 30441401376, 106445312312, 112304687432, 715332031056
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 5: 143, 30432, 214423, 3204322, 30444432, 3044444432, 43204443211, 322044443222, 4320444443211, 4432044432101.

Links

Crossrefs

Cf. A165032, A165044, A165036, A165037, A165041, A165039, A165049.
In other bases: Empty (base 2), A165004 (base 3), A165023 (base 4), A165062 (base 6), A165082 (base 7), A165101 (base 8), A165121 (base 9), A164720 (base 10).

A165048 a(n) = smallest number that leads to a new cycle under the base-5 Kaprekar map of A165032.

Original entry on oeis.org

0, 8, 27, 126, 626, 3126, 15626, 78126, 390626, 1953126, 9765626, 9765824, 48828126, 244140626, 244140699, 244141624, 1220703126, 1220703127, 6103515626, 6103515639, 6103515656, 6103515699, 6103515999, 6103520624
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 5: 0, 13, 102, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001.

Links

Crossrefs

Cf. A165032, A165037, A165049, A165050.
In other bases: A164887 (base 2), A165009 (base 3), A165029 (base 4), A165068 (base 6), A165087 (base 7), A165107 (base 8), A165127 (base 9), A151964 (base 10).

A165033 A165032(n)/4.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 4, 3, 2, 1, 0, 6, 6, 12, 18, 24, 6, 0, 6, 12, 18, 12, 6, 6, 12, 18, 18, 12, 12, 12, 18, 24, 18, 18, 18, 18, 12, 12, 12, 18, 24, 12, 6, 6, 12, 18, 12, 6, 0, 6, 12, 18, 12, 6, 6, 12, 24, 18, 12, 12, 12, 18, 18, 18, 18, 24, 18, 12, 12
Offset: 0

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165032.
In other bases: A164884 (base 2), A164994 (base 3), A165013 (base 4), A165052 (base 6), A165072 (base 7), A165091 (base 8), A165111 (base 9), A151950 (base 10).

A165034 Length of preperiodic part of trajectory of n under iteration of the base-5 Kaprekar map in A165032.

Original entry on oeis.org

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165032, A165035.
In other bases: A164885 (base 2), A164995 (base 3), A165014 (base 4), A165053 (base 6), A165073 (base 7), A165092 (base 8), A165112 (base 9), A151962 (base 10).

A165035 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-5 Kaprekar map in A165032.

Original entry on oeis.org

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165032, A165034.
In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165054 (base 6), A165074 (base 7), A165093 (base 8), A165113 (base 9), A151963 (base 10).

A165045 Number of cycles of n-digit numbers (including fixed points) under the base-5 Kaprekar map A165032.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 6, 3, 9, 2, 14, 2, 16, 4, 23, 4, 26, 4, 30, 5, 36, 7, 40, 11, 54, 11, 68, 14, 77, 16, 83, 18, 95, 19, 107, 25, 126, 27, 144, 29, 150, 30, 160, 33, 188, 35, 196, 41, 209, 42, 238, 46, 247, 50, 257, 63, 313, 64, 367, 78, 378, 82, 397, 91
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165032, A165037, A165046, A008617.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165006 (base 3), A165025 (base 4), A165064 (base 6), A165084 (base 7), A165103 (base 8), A165123 (base 9), A164731 (base 10).
Showing 1-10 of 29 results. Next

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