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 12 results. Next

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]

A164733 Number of n-digit fixed points under the Kaprekar map A151949.

Original entry on oeis.org

1, 0, 1, 1, 0, 2, 0, 2, 2, 3, 1, 5, 1, 6, 2, 8, 2, 12, 3, 14, 5, 17, 7, 21, 8, 25, 12, 30, 14, 36, 17, 43, 21, 49, 25, 58, 31, 66, 36, 75, 43, 85, 49, 96, 58, 109, 66, 121, 75, 136, 86, 150, 96, 167, 109, 184, 121, 202, 136, 222, 150, 242, 167, 265, 185, 287, 202, 313, 222, 338
Offset: 1

Views

Author

Joseph Myers, Aug 23 2009

Keywords

Links

Crossrefs

Cf. A151949, A099009, A164731, A164732, A164734, A164735, A164736.
Bisections: A309223, A309224.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A165027 (base 4), A008617 (base 5), A165066 (base 6), A008722 (base 7, conjecturally), A165105 (base 8), A165125 (base 9). [From Joseph Myers, Sep 05 2009]

Formula

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
a(n) = a(n-2) + a(n-6) - a(n-8) + a(n-9) - a(n-11) + a(n-14) - a(n-15) - a(n-16) + a(n-17) - a(n-20) + a(n-22) - a(n-23) + a(n-25) + a(n-29) - a(n-31) for n > 33.
G.f.: x*(-x^32 + x^31 - x^29 + x^28 - x^27 + x^26 - x^24 + 2*x^23 - x^22 + x^21 + x^20 + 2*x^18 - x^17 + x^16 + 2*x^15 - 3*x^14 + 2*x^13 - x^12 + x^11 - x^9 + 2*x^8 - x^6 + x^5 - x^4 + x^3 + 1)/(x^31 - x^29 - x^25 + x^23 - x^22 + x^20 - x^17 + x^16 + x^15 - x^14 + x^11 - x^9 + x^8 - x^6 - x^2 + 1). (End)

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)

A165064 Number of cycles of n-digit numbers (including fixed points) under the base-6 Kaprekar map A165051.

Original entry on oeis.org

1, 0, 1, 1, 2, 4, 1, 5, 2, 7, 3, 9, 4, 13, 7, 17, 8, 24, 11, 30, 16, 37, 21, 46, 27, 57, 34, 68, 42, 83, 52, 96, 64, 113, 77, 132, 90, 153, 107, 175, 125, 200, 145, 226, 168, 256, 191, 288, 217, 323, 247, 358, 278, 399, 312, 441, 348, 487, 387, 536, 429, 587, 475, 641
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165051, A165056, A165065, A165066.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165006 (base 3), A165025 (base 4), A165045 (base 5), A165084 (base 7), A165103 (base 8), A165123 (base 9), A164731 (base 10).

Formula

G.f.: x*(1 + x + 2*x^5 - 2*x^7 - 3*x^8 - 3*x^9 - x^10 + 2*x^11 + 4*x^12 + 4*x^13 + 4*x^14 + x^15 - 3*x^16 - 3*x^17 - 2*x^18 - x^19 + x^21 + x^22) / ((1 - x)^4*(1 + x)^3*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) (conjectured). - Colin Barker, Jun 01 2017

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).

A165006 Number of cycles of n-digit numbers (including fixed points) under the base-3 Kaprekar map A164993.

Original entry on oeis.org

1, 0, 0, 1, 1, 1, 2, 1, 3, 2, 5, 2, 6, 3, 7, 4, 10, 5, 12, 6, 13, 7, 16, 8, 17, 9, 19, 10, 22, 11, 23, 14, 26, 15, 30, 16, 33, 18, 34, 19, 37, 20, 39, 23, 42, 24, 47, 25, 48, 26, 50, 28, 55, 29, 56, 32, 59, 33, 63, 34, 64, 37, 65, 40, 72, 41, 78, 44, 79, 46, 82, 49, 83, 51, 87, 52
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A164993, A164998, A165007, A008615.
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165025 (base 4), A165045 (base 5), A165064 (base 6), A165084 (base 7), A165103 (base 8), A165123 (base 9), A164731 (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).

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).

A165123 Number of cycles of n-digit numbers (including fixed points) under the base-9 Kaprekar map A165110.

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 1, 2, 2, 3, 2, 3, 3, 3, 4, 2, 4, 4, 5, 4, 6, 5, 9, 4, 15, 4, 15, 5, 18, 5, 19, 7, 23, 5, 30, 6, 32, 8, 32, 8, 34, 11, 34, 11, 39, 12, 42, 14, 43, 15, 44, 17, 50, 19, 54, 22, 57, 22, 63, 21, 64, 23, 68, 29, 95, 26, 127, 34, 130, 34
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165110, A165115, A165124, A165125.
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), A165103 (base 8), A164731 (base 10).

A164734 Number of n-digit cycles of length 2 under the Kaprekar map A151949.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 2, 1, 1, 1, 1, 1, 0, 3, 0, 3, 0, 2, 0, 2, 3, 1, 2, 1, 2, 1, 1, 4, 1, 4, 0, 3, 0, 3, 4, 2, 3, 2, 3, 1, 2, 5, 2, 5, 1, 4, 1, 4, 5, 3, 4, 3, 4, 2, 3, 7, 3, 6, 2, 5, 2, 5, 7, 4, 6, 4, 5, 3, 4, 9, 4, 8, 3, 7, 3, 6, 9, 5, 8, 5, 7, 4
Offset: 1

Views

Author

Joseph Myers, Aug 23 2009

Keywords

Links

Crossrefs

Cf. A151949, A164723, A164724, A164731, A164732, A164733, A164735, A164736.

Formula

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
a(n) = a(n-7) + a(n-9) + a(n-14) - a(n-16) - a(n-21) - a(n-23) + a(n-30) for n > 41.
G.f.: x*(-x^40 - x^38 - x^36 + x^33 - x^32 + 2*x^31 - x^30 + 2*x^29 - x^28 + x^27 + x^25 - x^24 + 2*x^23 - x^22 + 2*x^21 - 2*x^20 + x^19 - x^16 - x^15 - x^14 + x^13 - x^12 + x^11 - x^4)/(x^30 - x^23 - x^21 - x^16 + x^14 + x^9 + x^7 - 1). (End)
Showing 1-10 of 12 results. Next

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

Content is available under The OEIS End-User License Agreement.