A165025 Number of cycles of n-digit numbers (including fixed points) under the base-4 Kaprekar map A165012.

1, 0, 1, 2, 1, 3, 1, 4, 3, 5, 4, 8, 5, 10, 8, 12, 10, 16, 12, 19, 16, 22, 19, 27, 22, 31, 27, 35, 31, 41, 35, 46, 41, 51, 46, 58, 51, 64, 58, 70, 64, 78, 70, 85, 78, 92, 85, 101, 92, 109, 101, 117, 109, 127, 117, 136, 127, 145, 136, 156, 145, 166, 156, 176, 166, 188, 176

Offset

1,4

Links

Joseph Myers, Table of n, a(n) for n=1..200

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

Conjectures from Colin Barker, Jun 01 2017: (Start)

G.f.: x*(1 - x^2 + x^3 - 2*x^6 + 3*x^8 - x^10) / ((1 - x)^3*(1 + x)^2*(1 + x + x^2)).

a(n) = 2*a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) + a(n-7) for n>7.

(End)

Crossrefs

Cf. A165012, A165017, A165026, A165027.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165006 (base 3), A165045 (base 5), A165064 (base 6), A165084 (base 7), A165103 (base 8), A165123 (base 9), A164731 (base 10).

Sequence in context: A098910 A291323 A290988 * A225045 A361736 A278575

Adjacent sequences: A165022 A165023 A165024 * A165026 A165027 A165028

Keyword

base,nonn

Author

Joseph Myers, Sep 04 2009

Status

approved