A165021 - OEIS

%I #10 Aug 28 2024 13:41:36

%S 0,30,126,201,570,2550,3369,3873,14565,41958,54441,62625,64641,171990,

%T 234405,254865,873129,954261,1004193,1036929,1044993,2788950,3755685,

%U 4083345,4165185,11140950,13978281,15285909,16075425,16399953,16599681

%N Consider the base-4 Kaprekar map n->K(n) defined in A165012. Sequence gives least elements of each cycle, including fixed points.

%C Initial terms in base 4: 0, 132, 1332, 3021, 20322, 213312, 310221, 330201, 3203211, 22033212.

%H Joseph Myers, <a href="/A165021/b165021.txt">Table of n, a(n) for n=1..7165</a>

%H Anthony Kay and Katrina Downes-Ward, <a href="https://arxiv.org/abs/2408.12257">Fixed Points and Cycles of the Kaprekar Transformation: 2. Even bases</a>, arXiv:2408.12257 [math.CO], 2024. See p. 16.

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

%Y Union of A165016 and A165023. Cf. A165012, A165022, A165017, A165019, A165030, A165025.

%Y In other bases: A163205 (base 2), A165002 (base 3), A165041 (base 5), A165060 (base 6), A165080 (base 7), A165099 (base 8), A165119 (base 9), A164718 (base 10).

%K base,nonn

%O 1,2

%A _Joseph Myers_, Sep 04 2009