A165066 Number of n-digit fixed points under the base-6 Kaprekar map A165051

1, 0, 1, 0, 1, 3, 0, 2, 1, 4, 2, 3, 2, 5, 4, 5, 3, 8, 4, 8, 6, 9, 7, 10, 8, 13, 9, 13, 10, 17, 12, 16, 14, 19, 16, 21, 16, 24, 19, 25, 21, 28, 23, 29, 26, 33, 27, 35, 29, 39, 33, 39, 35, 44, 38, 46, 40, 50, 43, 53, 46, 56, 50, 58, 53, 64, 55, 66, 59, 71, 63, 73, 66, 78, 71, 81, 73, 87

Offset

1,6

Links

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

Index entries for the Kaprekar map

Formula

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

a(n) = - a(n-1) + a(n-3) + 2*a(n-4) + 2*a(n-5) + a(n-6) - a(n-7) - 2*a(n-8) - 2*a(n-9) - a(n-10) + a(n-12) + a(n-13) for n > 15.

G.f.: x*(-x^14 + x^8 - x^5 + x^4 - x^2 - x - 1)/((x - 1)^3*(x + 1)^2*(x^2 + 1)*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Cf. A165051, A165055, A165064, A165065.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A165027 (base 4), A008617 (base 5), A008722 (base 7, conjecturally), A165105 (base 8), A165125 (base 9), A164733 (base 10).

Sequence in context: A329204 A375493 A268464 * A034389 A084196 A295041

Adjacent sequences: A165063 A165064 A165065 * A165067 A165068 A165069

Keyword

base,nonn

Author

Joseph Myers, Sep 04 2009

Status

approved