A164735 Number of n-digit cycles of length 3 under the Kaprekar map A151949.

0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 10, 0, 20, 0, 36, 0, 60, 1, 94, 4, 141, 10, 204, 21, 286, 39, 392, 66, 527, 105, 696, 159, 906, 231, 1164, 326, 1477, 449, 1854, 605, 2304, 801, 2836, 1044, 3462, 1341, 4194, 1701, 5044, 2133, 6027, 2646, 7158, 3252, 8452, 3963

Offset

1,10

Links

Joseph Myers, Table of n, a(n) for n = 1..70

M. Kauers and C. Koutschan, Some D-finite and some possibly D-finite sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023. [see page 45]

M. Kauers and C. Koutschan, Conjectured closed form for a(n), a quasi-polynomial of period 18 and degree 5.

Index entries for the Kaprekar map

Formula

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)

a(n) = 4*a(n-2) - 6*a(n-4) + 5*a(n-6) - 5*a(n-8) + a(n-9) + 6*a(n-10) - 4*a(n-11) - 4*a(n-12) + 6*a(n-13) + a(n-14) - 5*a(n-15) + 5*a(n-17) - 6*a(n-19) + 4*a(n-21) - a(n-23) for n > 25.

G.f.: x*(-x^24 + x^22 + x^18 - x^16 + x^15 - x^13 + x^7)/((x - 1)^6*(x + 1)^5*(x^2 - x + 1)*(x^2 + x + 1)^2*(x^6 + x^3 + 1)). (End)

Crossrefs

Cf. A151949, A164725, A164726, A164731, A164732, A164733, A164734, A164736.

Sequence in context: A174381 A184363 A331451 * A293933 A345057 A158976

Adjacent sequences: A164732 A164733 A164734 * A164736 A164737 A164738

Keyword

base,nonn

Author

Joseph Myers, Aug 23 2009

Status

approved