A165064 Number of cycles of n-digit numbers (including fixed points) under the base-6 Kaprekar map A165051.

1, 0, 1, 1, 2, 4, 1, 5, 2, 7, 3, 9, 4, 13, 7, 17, 8, 24, 11, 30, 16, 37, 21, 46, 27, 57, 34, 68, 42, 83, 52, 96, 64, 113, 77, 132, 90, 153, 107, 175, 125, 200, 145, 226, 168, 256, 191, 288, 217, 323, 247, 358, 278, 399, 312, 441, 348, 487, 387, 536, 429, 587, 475, 641

Offset

1,5

Links

Joseph Myers, Table of n, a(n) for n=1..100

H. Hanslik, E. Hetmaniok, I. Sobstyl, et al., Orbits of the Kaprekar's transformations-some introductory facts, Zeszyty Naukowe Politechniki Śląskiej, Seria: Matematyka Stosowana z. 5, Nr kol. 1945; 2015.

Index entries for the Kaprekar map

Formula

G.f.: x*(1 + x + 2*x^5 - 2*x^7 - 3*x^8 - 3*x^9 - x^10 + 2*x^11 + 4*x^12 + 4*x^13 + 4*x^14 + x^15 - 3*x^16 - 3*x^17 - 2*x^18 - x^19 + x^21 + x^22) / ((1 - x)^4*(1 + x)^3*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) (conjectured). - Colin Barker, Jun 01 2017

Crossrefs

Cf. A165051, A165056, A165065, A165066.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165006 (base 3), A165025 (base 4), A165045 (base 5), A165084 (base 7), A165103 (base 8), A165123 (base 9), A164731 (base 10).

Sequence in context: A060370 A318704 A303977 * A299918 A390470 A021418

Adjacent sequences: A165061 A165062 A165063 * A165065 A165066 A165067

Keyword

base,nonn

Author

Joseph Myers, Sep 04 2009

Status

approved