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.

Previous Showing 11-18 of 18 results.

A165128 Smallest member of cycle corresponding to n-th term of A165127.

Original entry on oeis.org

0, 16, 320, 2256, 3712, 34960, 41520, 183696, 3496800, 31596672, 31531872, 278474880, 326952560, 2066242576, 2516902752, 2598744000, 26531651360, 23087388720, 167365651216, 203869268832, 211282856832, 2184410558000
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 9: 0, 17, 385, 3076, 5074, 52854, 62853, 308876, 6518633, 65407433.

Links

Crossrefs

Cf. A165110, A165115, A165127, A165129.
In other bases: A163205 (base 2), A165010 (base 3), A165030 (base 4), A165049 (base 5), A165069 (base 6), A165088 (base 7), A165108 (base 8), A151965 (base 10).

A165129 Length of cycle corresponding to n-th term of A165127.

Original entry on oeis.org

1, 2, 2, 3, 3, 5, 1, 14, 2, 4, 1, 12, 1, 5, 4, 1, 6, 1, 6, 2, 2, 4, 6, 1, 11, 1, 1, 3, 4, 6, 1, 2, 1, 7, 1, 2, 1, 9, 6, 1, 1, 4, 4, 1, 1, 1, 15, 6, 1, 1, 6, 4, 7, 4, 1, 1, 10, 2, 2, 2, 1, 8, 3, 2, 7, 4, 1, 1, 1, 1, 2, 6, 1, 1, 3, 2, 6, 4, 6, 7, 3, 2, 8, 3, 7, 4, 1, 1, 1, 2, 13, 1, 1, 20, 4, 5, 1, 2, 3, 6, 2, 8
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Links

Crossrefs

Cf. A165110, A165115, A165127, A165128.
In other bases: A000012 (base 2), A165011 (base 3), A165031 (base 4), A165050 (base 5), A165070 (base 6), A165089 (base 7), A165109 (base 8), A151966 (base 10).

A165119 Consider the base-9 Kaprekar map n->K(n) defined in A165110. Sequence gives least elements of each cycle, including fixed points.

Original entry on oeis.org

0, 16, 320, 2256, 3712, 34960, 41520, 183696, 3496800, 31531872, 31596672, 278474880, 326952560, 2066242576, 2516902752, 2598744000, 23087388720, 26531651360, 167365651216, 203869268832, 211282856832, 1901588877840
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 9: 0, 17, 385, 3076, 5074, 52854, 62853, 308876, 6518633, 65288533.

Links

Crossrefs

Union of A165114 and A165121. Cf. A165110, A165120, A165115, A165117, A165128, A165123.
In other bases: A163205 (base 2), A165002 (base 3), A165021 (base 4), A165041 (base 5), A165060 (base 6), A165080 (base 7), A165099 (base 8), A164718 (base 10).

A165121 Consider the base-9 Kaprekar map n->K(n) defined in A165110. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

16, 320, 2256, 3712, 34960, 183696, 3496800, 31596672, 278474880, 2066242576, 2516902752, 26531651360, 167365651216, 203869268832, 211282856832, 2145190286000, 2184410558000, 16513410921312, 176898519791120
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 9: 17, 385, 3076, 5074, 52854, 308876, 6518633, 65407433, 641888643, 5288888854.

Links

Crossrefs

Cf. A165110, A165122, A165114, A165115, A165119, A165117, A165128.
In other bases: Empty (base 2), A165004 (base 3), A165023 (base 4), A165043 (base 5), A165062 (base 6), A165082 (base 7), A165101 (base 8), A164720 (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).

A165127 a(n) = smallest number that leads to a new cycle under the base-9 Kaprekar map of A165110.

Original entry on oeis.org

0, 12, 83, 730, 731, 6562, 6591, 59050, 531442, 4782970, 4783971, 43046722, 43046723, 387420490, 387420491, 387429540, 3486784402, 3486852471, 31381059610, 31381059611, 31381059801, 282429536482, 282429536492
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 9: 0, 13, 102, 1001, 1002, 10001, 10033, 100001, 1000001, 10000001.

Links

Crossrefs

Cf. A165110, A165115, A165128, A165129.
In other bases: A164887 (base 2), A165009 (base 3), A165029 (base 4), A165048 (base 5), A165068 (base 6), A165087 (base 7), A165107 (base 8), A151964 (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).

A165126 Consider the base-9 Kaprekar map x->K(x) described in A165110. Sequence gives the smallest number that belongs to a cycle of length n under repeated iteration of this map, or -1 if there is no cycle of length n.

Original entry on oeis.org

0, 16, 2256, 31596672, 34960, 26531651360, 14560721001508880, 8724454714749973651840, 108401672318914272, 711223428647787942432, 16513410921312, 278474880, 4754966263206652084045296, 183696
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Known values (to 70 base-9 digits):
a(1) = 0 (base 10) = 0 (base 9)
a(2) = 16 (base 10) = 17 (base 9)
a(3) = 2256 (base 10) = 3076 (base 9)
a(4) = 31596672 (base 10) = 65407433 (base 9)
a(5) = 34960 (base 10) = 52854 (base 9)
a(6) = 26531651360 (base 10) = 75430875432 (base 9)
a(7) = 14560721001508880 (base 10) = 77643208887654212 (base 9)
a(8) = 8724454714749973651840 (base 10) = 87654320888888876543211 (base 9)
a(9) = 108401672318914272 (base 10) = 644444418864444443 (base 9)
a(10) = 711223428647787942432 (base 10) = 6444444441886444444443 (base 9)
a(11) = 16513410921312 (base 10) = 64418888886443 (base 9)
a(12) = 278474880 (base 10) = 641888643 (base 9)
a(13) = 4754966263206652084045296 (base 10) = 65544444218888886644444333 (base 9)
a(14) = 183696 (base 10) = 308876 (base 9)
a(15) = 8780535458788649952 (base 10) = 64444441888864444443 (base 9)
a(16) = 8811048483031324779456676539593726674416 (base 10) = 655444442188888888888888888888886644444333 (base 9)
a(18) = 177097392902234856396140027020301600 (base 10) = 7766644432208888888888888766544422212 (base 9)
a(20) = 50771339309018227821951440 (base 10) = 776444432088888887654444212 (base 9)
a(21) = 124998824875093374012011515622478472976 (base 10) = 7544444444444421888888886644444444444432 (base 9)
a(22) = 31197333902107825741164471552 (base 10) = 655444444444308875444444444333 (base 9)
a(23) = 685322163857921701893212141347733334983278765142051291692546183840 (base 10) = 876544444444444432088888888888888888888888888888887654444444444443211 (base 9)
a(25) = 702826002884083319045760971727413317645857409225018391041723392 (base 10) = 655444444444444444443088888888888888888888887544444444444444444333 (base 9)
a(27) = 94116815581356594318021072974737787790560 (base 10) = 7766644432208888888888888888888766544422212 (base 9)
a(28) = 2156904722606587695378609845389399883833898563216184240 (base 10) = 777777655554444333332222210888776666655555444433332111112 (base 9)
a(29) = 26981972242036651232570366433200 (base 10) = 776444444443208888876544444444212 (base 9)
a(31) = 377773874412068206712875872 (base 10) = 6441888888888888888888886443 (base 9)
a(35) = 2520442200659768347220271484032 (base 10) = 65408888888888888888888888887433 (base 9)
a(39) = 1161485426793562822354375723686123973520 (base 10) = 77644444320888888888888888888876544444212 (base 9)
a(40) = 16327050854444484146838503988925985281714578428892247536 (base 10) = 6554444444444444444444442188888866444444444444444444444333 (base 9)
a(46) = 10150412679066664692018845810715370585139195588212689167959856 (base 10) = 7665444444444444444444444422218888666644444444444444444444443222 (base 9)
a(65) = 26152889553714885216926446303415314330076524215805520 (base 10) = 7654308888888888888888888888888888888888888888888754322 (base 9)

Links

Crossrefs

Cf. A165110, A165114, A165115, A165117, A165119, A165121.
In other bases: A153881 (base 2), A165008 (base 3), A165028 (base 4), A165047 (base 5), A165067 (base 6), A165086 (base 7), A165106 (base 8), A151959 (base 10).
Previous Showing 11-18 of 18 results.

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