A165027 Number of n-digit fixed points under the base-4 Kaprekar map A165012

1, 0, 1, 1, 0, 3, 1, 3, 3, 5, 3, 8, 5, 9, 8, 12, 9, 16, 12, 18, 16, 22, 18, 27, 22, 30, 27, 35, 30, 41, 35, 45, 41, 51, 45, 58, 51, 63, 58, 70, 63, 78, 70, 84, 78, 92, 84, 101, 92, 108, 101, 117, 108, 127, 117, 135, 127, 145, 135, 156, 145, 165, 156, 176, 165, 188, 176, 198

Offset

1,6

Links

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

Index entries for the Kaprekar map

Formula

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

a(n) = 2*a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) + a(n-7) for n > 8.

G.f.: x*(x^7 - x^6 - 2*x^5 + x^4 + x^2 - 1)/((x - 1)^3*(x + 1)^2*(x^2 + x + 1)). (End)

Crossrefs

Cf. A165012, A165016, A165025, A165026.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A008617 (base 5), A165066 (base 6), A008722 (base 7, conjecturally), A165105 (base 8), A165125 (base 9), A164733 (base 10).

Sequence in context: A145015 A085723 A186422 * A342341 A078555 A259286

Adjacent sequences: A165024 A165025 A165026 * A165028 A165029 A165030

Keyword

base,nonn,changed

Author

Joseph Myers, Sep 04 2009

Status

approved