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 11-15 of 15 results.

A165000 Consider the base-3 Kaprekar map n->K(n) defined in A164993. Sequence gives numbers belonging to cycles of length greater than 1.

Original entry on oeis.org

32, 52, 320, 484, 580, 1696, 1768, 15304, 16024, 16240, 18208, 18424, 26240, 39364, 48100, 48964, 137776, 144328, 147136, 164008, 166168, 166816, 172720, 173368, 433012, 441652, 1240024, 1299064, 1318720, 1325200, 1327144, 1476208, 1495864
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 3: 1012, 1221, 102212, 122221, 210111, 2022211, 2102111, 202222211, 210222111, 211021111.

Links

Crossrefs

Cf. A164993, A165001, A164997, A164998, A165002, A165004, A165010.
In other bases: Empty (base 2), A165019 (base 4), A165039 (base 5), A165058 (base 6), A165078 (base 7), A165097 (base 8), A165117 (base 9), A099010 (base 10).

A165002 Consider the base-3 Kaprekar map n->K(n) defined in A164993. Sequence gives least elements of each cycle, including fixed points.

Original entry on oeis.org

0, 32, 184, 320, 1696, 2008, 5332, 15304, 18208, 19144, 26240, 55360, 137776, 146488, 164008, 172720, 175528, 433012, 520372, 1240024, 1476208, 1502344, 1554904, 1581040, 1589464, 3975844, 4487680, 4749760, 11160256, 13286008
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 3: 0, 1012, 20211, 102212, 2022211, 2202101, 21022111, 202222211, 220222101, 222021001.

Links

Crossrefs

Union of A164997 and A165004. Cf. A164993, A165003, A164998, A165000, A165010, A165006.
In other bases: A163205 (base 2), A165021 (base 4), A165041 (base 5), A165060 (base 6), A165080 (base 7), A165099 (base 8), A165119 (base 9), A164718 (base 10).

A165004 Consider the base-3 Kaprekar map n->K(n) defined in A164993. Sequence gives least elements of each cycle of length > 1.

Original entry on oeis.org

32, 320, 1696, 15304, 18208, 26240, 137776, 164008, 172720, 433012, 1240024, 1476208, 1554904, 1581040, 4487680, 11160256, 13286008, 13994560, 14230648, 14309056, 35075092, 42160852, 100442344, 106819600, 119574208, 125951464
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Initial terms in base 3: 1012, 102212, 2022211, 202222211, 220222101, 1022222212, 20222222211, 22022222101, 22202221001, 210222222111.

Links

Crossrefs

Cf. A164993, A165005, A164997, A164998, A165002, A165000, A165010.
In other bases: Empty (base 2), A165023 (base 4), A165043 (base 5), A165062 (base 6), A165082 (base 7), A165101 (base 8), A165121 (base 9), A164720 (base 10).

A165008 Consider the base-3 Kaprekar map x->K(x) described in A164993. 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, 32, 320, 26240, 1240024, 11160256, 2297798771761759543384, 15075857741528904364175224, 8135830264, 5931020266096, 659002251784, 350220815692997944
Offset: 1

Views

Author

Joseph Myers, Sep 04 2009

Keywords

Comments

Known values (to 200 base-3 digits):
a(1) = 0 (base 10) = 0 (base 3)
a(2) = 32 (base 10) = 1012 (base 3)
a(3) = 320 (base 10) = 102212 (base 3)
a(4) = 26240 (base 10) = 1022222212 (base 3)
a(5) = 1240024 (base 10) = 2022222222211 (base 3)
a(6) = 11160256 (base 10) = 202222222222211 (base 3)
a(7) = 2297798771761759543384 (base 10) = 202222222222222222222222222222222222222222211 (base 3)
a(8) = 15075857741528904364175224 (base 10) = 20222222222222222222222222222222222222222222222222211 (base 3)
a(9) = 8135830264 (base 10) = 202222222222222222211 (base 3)
a(10) = 5931020266096 (base 10) = 202222222222222222222222211 (base 3)
a(11) = 659002251784 (base 10) = 2022222222222222222222211 (base 3)
a(12) = 350220815692997944 (base 10) = 2022222222222222222222222222222222211 (base 3)
a(14) = 480412641554176 (base 10) = 2022222222222222222222222222211 (base 3)
a(15) = 1202547548374693105751742636119782969638250884664 (base 10) = 20222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(18) = 3151987341236981536 (base 10) = 202222222222222222222222222222222222211 (base 3)
a(20) = 1221144477063841253498193544 (base 10) = 202222222222222222222222222222222222222222222222222222211 (base 3)
a(21) = 1675095304614322707130576 (base 10) = 202222222222222222222222222222222222222222222222211 (base 3)
a(22) = 5840696178317563736403001300866976 (base 10) = 20222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(23) = 186121700512702523014504 (base 10) = 2022222222222222222222222222222222222222222222211 (base 3)
a(24) = 133616394263854789527971404013309218848694542736 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(26) = 135682719673760139277577056 (base 10) = 2022222222222222222222222222222222222222222222222222211 (base 3)
a(27) = 3103985417701264389637747414334049249616 (base 10) = 20222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(28) = 2262805369504221740045917865049521902973704 (base 10) = 20222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(29) = 98912702642171141533353677464 (base 10) = 2022222222222222222222222222222222222222222222222222222222211 (base 3)
a(30) = 890214323779540273800183097216 (base 10) = 202222222222222222222222222222222222222222222222222222222222211 (base 3)
a(33) = 648966242035284859600333477874104 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(34) = 1624463421305399727955317383718278234275809671395357663852488383536 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(35) = 52566265604858073627627011707802824 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(36) = 14846266029317198836441267112589913205410504744 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(39) = 344887268633473821070860823814894361064 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(40) = 1166199021234168600322186441674903634837253284669268066647739969989548815584492779042071704 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(41) = 27935868759311379506739726729006443246584 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(42) = 95922940564662548536033536191180611455752285286224474692825586559712504 (base 10) = 20222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(44) = 51765728804119417583918760520852820074569256760349620344 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(46) = 131581537125737377964380708081180536976340583383023970772051559066816 (base 10) = 20222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(48) = 850159086479708909634873915981004749796357644523896420586202438122381086561095235921670275856 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(50) = 10822927935372237951765683725078046726744257962016 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(51) = 97406351418350141565891153525702420540698321658184 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(52) = 50977383456624829456538198506977215332656450244796421055229922546880175495464 (base 10) = 20222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(53) = 7889914464886361466837183435581896063796564054313304 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(55) = 37737216298203055418676776419701705834360988178294873234416 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(60) = 1184233834131636401679426372730624832787065250447215736948464031601384 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(65) = 2228344885192592219417444970806966027813181990940133969619325624 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(69) = 14620170791748597551597856453464504108482287042558218974672395451864 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(74) = 863306465081962936824301825720625503101770567576020272235430279037412576 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(78) = 3010163515730239554579124083638497588178030730504983866890271696470727482831948976 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(81) = 4129168059986611185979594079065154441945172469828510105473623726297294215132984 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(83) = 334462612858915506064347120404277509797558970056109318543363521830080831425772104 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(86) = 243823244774149403920909050774718304642420489170903693218112007414128926109387867456 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(89) = 177747145440354915458342698014769644084324536605588792356003653404899987133743755379064 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(90) = 1599724308963194239125084282132926796758920829450299131204032880644099884203693798411616 (base 10) = 202222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(95) = 94462120719967656626097101775667194421817516058210713398466937569153454062343915102407808424 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)
a(98) = 68862886004856421680424787194461384733504969206435610067482397487912868011448714109655292344736 (base 10) = 2022222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211 (base 3)

Links

Crossrefs

Cf. A164993, A164997, A164998, A165000, A165002, A165004.
In other bases: A153881 (base 2), A165028 (base 4), A165047 (base 5), A165067 (base 6), A165086 (base 7), A165106 (base 8), A165126 (base 9), A151959 (base 10).

A319798 Smallest fixed points (>0) of the base-n Kaprekar map.

Original entry on oeis.org

9, 184, 30, 8, 105, 1922263344, 21, 41520, 495, 40, 858, 3488424, 65, 30996, 2040, 96, 2907, 264925230120, 133, 2787400, 5313, 176, 6900, 237360, 225, 9742824, 10962, 280, 13485, 763713003420, 341, 26485184, 19635, 408, 23310, 107599353444576, 481, 60920080, 31980
Offset: 2

Views

Author

Seiichi Manyama, Sep 28 2018

Keywords

Comments

Conjecture: If n = 3*k - 1 (>2), a(n) = A000567(k). For example, a(29) = 10 * (3*10 - 2) = 280.

Links

Crossrefs

Cf. A000567, A099009, A163205, A164997, A165016, A165036, A165055, A165075, A165094, A165114, A319839.

Extensions

a(19) and a(31)-a(40) from Giovanni Resta, Oct 02 2018
Previous Showing 11-15 of 15 results.

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

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