A165047 Consider the base-5 Kaprekar map x->K(x) described in A165032. 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.

0, 48, 45781056, 1992, 7488, 249992, 26648194761946797370910644531056, 170312312, 447082519531056, 953674316406249992, 43487548828124832, 68219378590583801269531056

Offset: 1

Author

Joseph Myers, Sep 04 2009

Keywords

• base
• nonn

Comments

Known values (to 100 base-5 digits):

a(1) = 0 (base 10) = 0 (base 5)

a(2) = 48 (base 10) = 143 (base 5)

a(3) = 45781056 (base 10) = 43204443211 (base 5)

a(4) = 1992 (base 10) = 30432 (base 5)

a(5) = 7488 (base 10) = 214423 (base 5)

a(6) = 249992 (base 10) = 30444432 (base 5)

a(7) = 26648194761946797370910644531056 (base 10) = 432044444444444444444444444444444444444443211 (base 5)

a(8) = 170312312 (base 10) = 322044443222 (base 5)

a(9) = 447082519531056 (base 10) = 432044444444444443211 (base 5)

a(10) = 953674316406249992 (base 10) = 30444444444444444444444432 (base 5)

a(11) = 43487548828124832 (base 10) = 331044444444444444443312 (base 5)

a(12) = 68219378590583801269531056 (base 10) = 4320444444444444444444444444444443211 (base 5)

a(13) = 388774887899923005107893914100714027881532907485961914056 (base 10) = 432222222222222222222222044444444444444444444444444444443222222222222222222222211 (base 5)

a(14) = 4366040229797363281056 (base 10) = 4320444444444444444444444443211 (base 5)

a(15) = 15550995515996920287582474884401599410921335220336914056 (base 10) = 4322222222222222222222222222222222044444444432222222222222222222222222222222211 (base 5)

a(18) = 1705484464764595031738281056 (base 10) = 432044444444444444444444444444444443211 (base 5)

a(20) = 6505906924303417326882481575012207031056 (base 10) = 432044444444444444444444444444444444444444444444444443211 (base 5)

a(21) = 416378043155418708920478820800781056 (base 10) = 432044444444444444444444444444444444444444444443211 (base 5)

a(22) = 39708904567281599895522958831861615180969238281056 (base 10) = 43204444444444444444444444444444444444444444444444444444444444444443211 (base 5)

a(23) = 16655121726216748356819152832031056 (base 10) = 4320444444444444444444444444444444444444444443211 (base 5)

a(24) = 1479271969470441337508073405618280737883196707116439938545227050781056 (base 10) = 432044444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443211 (base 5)

a(26) = 260236276972136693075299263000488281056 (base 10) = 4320444444444444444444444444444444444444444444444443211 (base 5)

a(27) = 9694556779121484349492909871059964643791317939758300781056 (base 10) = 43204444444444444444444444444444444444444444444444444444444444444444444444444443211 (base 5)

a(28) = 151477449673773192960826716735311947559239342808723449707031056 (base 10) = 43204444444444444444444444444444444444444444444444444444444444444444444444444444444443211 (base 5)

a(29) = 4066191827689635829301550984382629394531056 (base 10) = 4320444444444444444444444444444444444444444444444444444443211 (base 5)

a(30) = 101654795692240895732538774609565734863281056 (base 10) = 432044444444444444444444444444444444444444444444444444444443211 (base 5)

a(33) = 1588356182691263995820918353274464607238769531056 (base 10) = 432044444444444444444444444444444444444444444444444444444444444443211 (base 5)

a(35) = 992722614182039997388073970796540379524230957031056 (base 10) = 4320444444444444444444444444444444444444444444444444444444444444444443211 (base 5)

a(36) = 59170878778817653500322936224731229515327868284657597541809082031056 (base 10) = 4320444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443211 (base 5)

a(39) = 387782271164859373979716394842398585751652717590332031056 (base 10) = 432044444444444444444444444444444444444444444444444444444444444444444444444443211 (base 5)

a(41) = 242363919478037108737322746776499116094782948493957519531056 (base 10) = 4320444444444444444444444444444444444444444444444444444444444444444444444444444443211 (base 5)

Links

• Joseph Myers, Table of n, a(n) for n=1..15
• Index entries for the Kaprekar map

Crossrefs

Cf. A165032, A165036, A165037, A165039, A165041, A165043.

In other bases: A153881 (base 2), A165008 (base 3), A165028 (base 4), A165067 (base 6), A165086 (base 7), A165106 (base 8), A165126 (base 9), A151959 (base 10).