This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165125 #9 Jun 02 2025 02:03:57 %S A165125 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 A165125 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 A165125 8,8 %N A165125 Number of n-digit fixed points under the base-9 Kaprekar map A165110. %H A165125 <a href="/index/K#Kaprekar_map">Index entries for the Kaprekar map</a> %F A165125 Conjectures from _Chai Wah Wu_, Apr 13 2024: (Start) %F A165125 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 A165125 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 A165125 Cf. A165110, A165114, A165123, A165124. %Y A165125 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 A165125 base,nonn %O A165125 1,14 %A A165125 _Joseph Myers_, Sep 04 2009