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 10 results.

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).

A164732 Number of n-digit numbers in a cycle (including fixed points) under the Kaprekar map A151949.

Original entry on oeis.org

1, 0, 1, 1, 10, 9, 8, 12, 16, 22, 14, 42, 18, 73, 29, 125, 34, 199, 38, 308, 49, 462, 71, 665, 105, 920, 161, 1243, 249, 1658, 379, 2170, 555, 2806, 780, 3587, 1075, 4539, 1449, 5689, 1922, 7059, 2516, 8677, 3252, 10566, 4156, 12774, 5255, 15337, 6578, 18300
Offset: 1

Views

Author

Joseph Myers, Aug 23 2009

Keywords

Links

Crossrefs

Cf. A151949, A164716, A164731, A164733, A164734, A164735, A164736.
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), A165104 (base 8), A165124 (base 9). [Joseph Myers, Sep 05 2009]

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)

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).

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).

A165124 Number of n-digit numbers in a cycle (including fixed points) under the base-9 Kaprekar map A165110.

Original entry on oeis.org

1, 2, 2, 6, 6, 14, 2, 5, 13, 10, 7, 10, 11, 13, 14, 3, 11, 17, 11, 23, 23, 17, 28, 10, 58, 17, 69, 40, 71, 38, 83, 43, 125, 26, 139, 17, 154, 23, 167, 42, 202, 71, 204, 34, 209, 65, 227, 45, 212, 62, 223, 86, 243, 77, 317, 90, 310, 125, 324, 83, 363, 86, 346, 159, 492, 124
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165110, A165115, A165123, A165125.
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), A165104 (base 8), A164732 (base 10).

A165007 Number of n-digit numbers in a cycle (including fixed points) under the base-3 Kaprekar map A164993.

Original entry on oeis.org

1, 0, 0, 2, 1, 3, 3, 1, 6, 5, 10, 3, 15, 4, 21, 7, 28, 12, 36, 11, 45, 13, 55, 18, 66, 19, 78, 25, 91, 28, 105, 35, 120, 41, 136, 43, 153, 47, 171, 56, 190, 58, 210, 68, 231, 73, 253, 84, 276, 85, 300, 97, 325, 103, 351, 116, 378, 119, 406, 133, 435, 140, 465, 155, 496, 162
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A164993, A164998, A165006, A008615.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165026 (base 4), A165046 (base 5), A165065 (base 6), A165085 (base 7), A165104 (base 8), A165124 (base 9), A164732 (base 10).

A165046 Number of n-digit numbers in a cycle (including fixed points) under the base-5 Kaprekar map A165032.

Original entry on oeis.org

1, 1, 2, 1, 4, 5, 4, 6, 1, 4, 4, 8, 9, 9, 21, 10, 29, 6, 48, 4, 66, 14, 93, 20, 126, 19, 166, 17, 214, 27, 270, 34, 339, 36, 410, 46, 495, 55, 591, 70, 699, 82, 819, 97, 952, 107, 1103, 135, 1260, 142, 1436, 175, 1628, 183, 1836, 231, 2061, 232, 2304, 288, 2565, 300
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165032, A165037, A165045, A008617.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165007 (base 3), A165026 (base 4), A165065 (base 6), A165085 (base 7), A165104 (base 8), A165124 (base 9), A164732 (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).

A165027 Number of n-digit fixed points under the base-4 Kaprekar map A165012.

Original entry on oeis.org

1, 0, 1, 1, 0, 3, 1, 3, 3, 5, 3, 8, 5, 9, 8, 12, 9, 16, 12, 18, 16, 22, 18, 27, 22, 30, 27, 35, 30, 41, 35, 45, 41, 51, 45, 58, 51, 63, 58, 70, 63, 78, 70, 84, 78, 92, 84, 101, 92, 108, 101, 117, 108, 127, 117, 135, 127, 145, 135, 156, 145, 165, 156, 176, 165, 188, 176, 198
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165012, A165016, A165025, A165026.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A008617 (base 5), A165066 (base 6), A008722 (base 7, conjecturally), A165105 (base 8), A165125 (base 9), A164733 (base 10).

Formula

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
a(n) = 2*a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) + a(n-7) for n > 8.
G.f.: x*(x^7 - x^6 - 2*x^5 + x^4 + x^2 - 1)/((x - 1)^3*(x + 1)^2*(x^2 + x + 1)). (End)
Showing 1-10 of 10 results.

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