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.

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

Offset: 1

Author

Joseph Myers, Sep 04 2009

Keywords

• base
• nonn

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

• Joseph Myers, Table of n, a(n) for n=1..16
• Index entries for the Kaprekar map

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).