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%I #11 Sep 21 2017 04:01:31
%S 10100,11100001,11111011010,1111110111101,1111101110011110,
%T 111010001110001001,110011110000010000010,10100101110110101001,
%U 1110100101000001111001010000,111010111010100100100000111,111101010011100000011010100
%N Trajectory of binary number 10100 (decimal 20) under the operation "Reverse and Add" carried out with complex base -1+i.
%H Kerry Mitchell, <a href="/A193241/b193241.txt">Table of n, a(n) for n = 0..500</a>
%H W. J. Gilbert, <a href="https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/arithmetic-in-complex-bases">Arithmetic in Complex Bases</a>, Mathematics Magazine, Vol. 57, No. 2 (Mar., 1984), pp. 77-81.
%e The initial term is 10100. Using complex base -1+i, this is -4-2i. Reversing 10100 gives 00101, which is 1-2i. Adding both terms gives -3-4i, which is 11100001, the second term.
%Y Cf A193239, number of steps needed to reach a palindrome with complex base -1+i. For that sequence, a(20)=-1, showing that decimal 20 (binary 10100) seems to not reach a palindrome under the "Reverse and Add" iteration. Cf A193240, the trajectory of 110 (decimal 6) under the "Reverse and Add" iteration with complex base -1+i.
%K nonn,base
%O 0,1
%A _Kerry Mitchell_, Jul 19 2011
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