A165125 Number of n-digit fixed points under the base-9 Kaprekar map A165110

1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 2, 2, 3, 2, 2, 1, 4, 2, 3, 2, 3, 3, 4, 2, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 6, 5, 7, 6, 7, 6, 6, 6, 8, 6, 7, 7, 8, 8, 8, 7, 7, 9, 8, 8

Offset

1,14

Links

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

Index entries for the Kaprekar map

Formula

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

a(n) = a(n-2) - a(n-3) + a(n-5) - a(n-6) + a(n-8) + a(n-15) - a(n-17) + a(n-18) - a(n-20) + a(n-21) - a(n-23) for n > 24.

G.f.: x*(x^23 + x^22 - x^21 + x^20 + 2*x^19 - x^18 + x^17 + 3*x^16 - 2*x^15 + 3*x^13 - x^12 + 2*x^10 - x^9 + 2*x^7 - x^5 + x^4 + x^3 - x^2 + 1)/(x^23 - x^21 + x^20 - x^18 + x^17 - x^15 - x^8 + x^6 - x^5 + x^3 - x^2 + 1). (End)

Crossrefs

Cf. A165110, A165114, A165123, A165124.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A165027 (base 4), A008617 (base 5), A165066 (base 6), A008722 (base 7, conjecturally), A165105 (base 8), A164733 (base 10).

Sequence in context: A133114 A156265 A232992 * A235187 A029333 A029261

Adjacent sequences: A165122 A165123 A165124 * A165126 A165127 A165128

Keyword

base,nonn,changed

Author

Joseph Myers, Sep 04 2009

Status

approved