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

A165076 Consider the base-7 Kaprekar map n->K(n) defined in A165071. Sequence gives numbers belonging to cycles, including fixed points.

Original entry on oeis.org

0, 144, 192, 1068, 1752, 1836, 9936, 10608, 13008, 13680, 15072, 55500, 72012, 77388, 89112, 91212, 91800, 640992, 643344, 660144, 674592, 760992, 780144, 3562968, 4605036, 4642668, 4772952, 5445336, 5464152, 31412208, 31680336
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 7: 0, 264, 363, 3054, 5052, 5232, 40653, 42633, 52632, 54612.

Links

Crossrefs

Union of A165075 and A165078. Cf. A165071, A165077, A165080, A165082, A165088, A165085.
In other bases: A163205 (base 2), A164998 (base 3), A165017 (base 4), A165037 (base 5), A165056 (base 6), A165095 (base 8), A165115 (base 9), A164716 (base 10).

A165075 List of fixed points of the base-7 Kaprekar map A165071.

Original entry on oeis.org

0, 1922263344, 94197649008, 96503566608, 4615731883344, 4728721980144, 4744863403344, 226171191723408, 231707706601008, 232498637278608, 232611627241008, 11082390700389744, 11353679929526544, 11392435533669744
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 7: 0, 65430653211, 6543206543211, 6654306532101, 654322065443211, 665432065432101, 666543065321001, 65432220654443211, 66543220654432101, 66654320654321001.

Links

Crossrefs

Cf. A165071, A165076, A165078, A008722.
In other bases: A163205 (base 2), A164997 (base 3), A165016 (base 4), A165036 (base 5), A165055 (base 6), A165094 (base 8), A165114 (base 9), A099009 (base 10).

A165078 Consider the base-7 Kaprekar map n->K(n) defined in A165071. Sequence gives numbers belonging to cycles of length greater than 1.

Original entry on oeis.org

144, 192, 1068, 1752, 1836, 9936, 10608, 13008, 13680, 15072, 55500, 72012, 77388, 89112, 91212, 91800, 640992, 643344, 660144, 674592, 760992, 780144, 3562968, 4605036, 4642668, 4772952, 5445336, 5464152, 31412208, 31680336, 32353344
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 7: 264, 363, 3054, 5052, 5232, 40653, 42633, 52632, 54612, 61641.

Links

Crossrefs

Cf. A165071, A165079, A165075, A165076, A165080, A165082, A165088.
In other bases: Empty (base 2), A165000 (base 3), A165019 (base 4), A165039 (base 5), A165058 (base 6), A165097 (base 8), A165117 (base 9), A099010 (base 10).

A165080 Consider the base-7 Kaprekar map n->K(n) defined in A165071. Sequence gives least elements of each cycle, including fixed points.

Original entry on oeis.org

0, 144, 1068, 9936, 55500, 640992, 3562968, 31412208, 220709400, 227429400, 228238488, 1922263344, 11150046252, 11432420652, 75796404672, 94197649008, 96503566608, 419850417612, 546394287000, 3939440152944, 4615731883344
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 7: 0, 264, 3054, 40653, 320544, 5306532, 42166443, 530666532, 5316666432, 5431055322.

Links

Crossrefs

Union of A165075 and A165082. Cf. A165071, A165081, A165076, A165078, A165088, A165084.
In other bases: A163205 (base 2), A165002 (base 3), A165021 (base 4), A165041 (base 5), A165060 (base 6), A165099 (base 8), A165119 (base 9), A164718 (base 10).

A165082 Consider the base-7 Kaprekar map n->K(n) defined in A165071. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

144, 1068, 9936, 55500, 640992, 3562968, 31412208, 220709400, 227429400, 228238488, 11150046252, 11432420652, 75796404672, 419850417612, 546394287000, 3939440152944, 26773614188652, 26884299308652
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 7: 264, 3054, 40653, 320544, 5306532, 42166443, 530666532, 5316666432, 5431055322, 5440665222.

Links

Crossrefs

Cf. A165071, A165083, A165075, A165076, A165080, A165078, A165088.
In other bases: Empty (base 2), A165004 (base 3), A165023 (base 4), A165043 (base 5), A165062 (base 6), A165101 (base 8), A165121 (base 9), A164720 (base 10).

A165087 a(n) = smallest number that leads to a new cycle under the base-7 Kaprekar map of A165071.

Original entry on oeis.org

0, 51, 344, 2402, 16808, 117650, 823544, 5764802, 40353608, 40353623, 40354466, 282475250, 1977326744, 1977326763, 13841287202, 13841287211, 13841290483, 96889010408, 96889010409, 678223072850, 678223072851, 678223072995
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 7: 0, 102, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 1000000022.

Links

Crossrefs

Cf. A165071, A165076, A165088, A165089.
In other bases: A164887 (base 2), A165009 (base 3), A165029 (base 4), A165048 (base 5), A165068 (base 6), A165107 (base 8), A165127 (base 9), A151964 (base 10).

A165073 Length of preperiodic part of trajectory of n under iteration of the base-7 Kaprekar map in A165071.

Original entry on oeis.org

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165071, A165074.
In other bases: A164885 (base 2), A164995 (base 3), A165014 (base 4), A165034 (base 5), A165053 (base 6), A165092 (base 8), A165112 (base 9), A151962 (base 10).

A165074 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-7 Kaprekar map in A165071.

Original entry on oeis.org

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

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165071, A165073.
In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165035 (base 5), A165054 (base 6), A165093 (base 8), A165113 (base 9), A151963 (base 10).

A165084 Number of cycles of n-digit numbers (including fixed points) under the base-7 Kaprekar map A165071.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 3, 2, 4, 2, 5, 1, 8, 6, 10, 5, 13, 7, 18, 7, 20, 8, 25, 12, 30, 13, 35, 15, 43, 16, 51, 20, 56, 25, 63, 29, 71, 33, 79, 38, 89, 42, 99, 48, 112, 53, 123, 57, 137, 63, 150, 71, 164, 79, 177, 87, 190, 95, 210, 101, 229, 109, 246, 119, 263, 132, 280
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165071, A165076, A165085, A008722.
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), A165103 (base 8), A165123 (base 9), A164731 (base 10).

A165085 Number of n-digit numbers in a cycle (including fixed points) under the base-7 Kaprekar map A165071.

Original entry on oeis.org

1, 0, 2, 3, 5, 6, 6, 6, 11, 6, 1, 7, 8, 11, 5, 14, 6, 2, 13, 19, 15, 11, 21, 17, 31, 32, 35, 16, 45, 42, 55, 31, 65, 34, 84, 24, 107, 45, 117, 39, 138, 54, 164, 53, 184, 67, 212, 70, 240, 81, 277, 90, 310, 97, 350, 108, 388, 125, 436, 140, 481, 155, 526, 179, 591, 181, 653
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165071, A165076, A165084, A008722.
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), A165104 (base 8), A165124 (base 9), A164732 (base 10).
Showing 1-10 of 29 results. Next

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