A165025 - OEIS

%I #17 Jun 02 2017 00:44:27

%S 1,0,1,2,1,3,1,4,3,5,4,8,5,10,8,12,10,16,12,19,16,22,19,27,22,31,27,

%T 35,31,41,35,46,41,51,46,58,51,64,58,70,64,78,70,85,78,92,85,101,92,

%U 109,101,117,109,127,117,136,127,145,136,156,145,166,156,176,166,188,176

%N Number of cycles of n-digit numbers (including fixed points) under the base-4 Kaprekar map A165012.

%H Joseph Myers, <a href="/A165025/b165025.txt">Table of n, a(n) for n=1..200</a>

%H H. Hanslik, E. Hetmaniok, I. Sobstyl, et al., <a href="http://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baztech-aeb2e2a6-99ca-4268-8f6b-a947b9c04da9">Orbits of the Kaprekar's transformations-some introductory facts</a>, Zeszyty Naukowe Politechniki Śląskiej, Seria: Matematyka Stosowana z. 5, Nr kol. 1945; 2015.

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

%F Conjectures from _Colin Barker_, Jun 01 2017: (Start)

%F G.f.: x*(1 - x^2 + x^3 - 2*x^6 + 3*x^8 - x^10) / ((1 - x)^3*(1 + x)^2*(1 + x + x^2)).

%F a(n) = 2*a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) + a(n-7) for n>7.

%F (End)

%Y Cf. A165012, A165017, A165026, A165027.

%Y In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A165006 (base 3), A165045 (base 5), A165064 (base 6), A165084 (base 7), A165103 (base 8), A165123 (base 9), A164731 (base 10).

%K base,nonn

%O 1,4

%A _Joseph Myers_, Sep 04 2009