A165125 - OEIS

%I #7 Apr 13 2024 22:53:55

%S 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,

%T 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,

%U 8,8

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

%H <a href="/index/K#Kaprekar_map">Index entries for the Kaprekar map</a>

%F Conjectures from _Chai Wah Wu_, Apr 13 2024: (Start)

%F 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.

%F 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)

%Y Cf. A165110, A165114, A165123, A165124.

%Y 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).

%K base,nonn

%O 1,14

%A _Joseph Myers_, Sep 04 2009