A193241 Trajectory of binary number 10100 (decimal 20) under the operation "Reverse and Add" carried out with complex base -1+i.
10100, 11100001, 11111011010, 1111110111101, 1111101110011110, 111010001110001001, 110011110000010000010, 10100101110110101001, 1110100101000001111001010000, 111010111010100100100000111, 111101010011100000011010100
Offset: 0
Examples
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.
Links
- Kerry Mitchell, Table of n, a(n) for n = 0..500
- W. J. Gilbert, Arithmetic in Complex Bases, Mathematics Magazine, Vol. 57, No. 2 (Mar., 1984), pp. 77-81.
Crossrefs
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.