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.

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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).

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 11-12 of 12 results.

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