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 A164733 #12 Jun 02 2025 01:52:19 %S A164733 1,0,1,1,0,2,0,2,2,3,1,5,1,6,2,8,2,12,3,14,5,17,7,21,8,25,12,30,14,36, %T A164733 17,43,21,49,25,58,31,66,36,75,43,85,49,96,58,109,66,121,75,136,86, %U A164733 150,96,167,109,184,121,202,136,222,150,242,167,265,185,287,202,313,222,338 %N A164733 Number of n-digit fixed points under the Kaprekar map A151949. %H A164733 Joseph Myers, <a href="/A164733/b164733.txt">Table of n, a(n) for n=1..70</a> %H A164733 <a href="/index/K#Kaprekar_map">Index entries for the Kaprekar map</a> %F A164733 Conjectures from _Chai Wah Wu_, Apr 13 2024: (Start) %F A164733 a(n) = a(n-2) + a(n-6) - a(n-8) + a(n-9) - a(n-11) + a(n-14) - a(n-15) - a(n-16) + a(n-17) - a(n-20) + a(n-22) - a(n-23) + a(n-25) + a(n-29) - a(n-31) for n > 33. %F A164733 G.f.: x*(-x^32 + x^31 - x^29 + x^28 - x^27 + x^26 - x^24 + 2*x^23 - x^22 + x^21 + x^20 + 2*x^18 - x^17 + x^16 + 2*x^15 - 3*x^14 + 2*x^13 - x^12 + x^11 - x^9 + 2*x^8 - x^6 + x^5 - x^4 + x^3 + 1)/(x^31 - x^29 - x^25 + x^23 - x^22 + x^20 - x^17 + x^16 + x^15 - x^14 + x^11 - x^9 + x^8 - x^6 - x^2 + 1). (End) %Y A164733 Cf. A151949, A099009, A164731, A164732, A164734, A164735, A164736. %Y A164733 Bisections: A309223, A309224. %Y A164733 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), A165125 (base 9). [From _Joseph Myers_, Sep 05 2009] %K A164733 base,nonn %O A164733 1,6 %A A164733 _Joseph Myers_, Aug 23 2009