@inproceedings{oai:ipsj.ixsq.nii.ac.jp:00097480,
 author = {Sakuta, Makoto and Araya, Makoto and Haque, Zahidul and Iida, Hiroyuki and Sakuta, Makoto and Araya, Makoto and Haque, Zahidul and Iida, Hiroyuki},
 book = {ゲームプログラミングワークショップ2001論文集},
 issue = {14},
 month = {Oct},
 note = {A two-times sorting sequence is constructed by calculating the next number with doubling the current number and sorting its digits into non-decreasing order. We propose the appropriate representation of a number with the arbitrary length of digits and the algorithms to calculate the sequence. Using this representation, we investigate two important properties of the sequence, i.e., cyclic and inductive. By the examination of the computer program, it is proved that every two-times sorting sequence falls onto a periodic cycle with the cyclic length 1, 2, 3, 4, 5, 6, or 12., A two-times sorting sequence is constructed by calculating the next number with doubling the current number and sorting its digits into non-decreasing order. We propose the appropriate representation of a number with the arbitrary length of digits and the algorithms to calculate the sequence. Using this representation, we investigate two important properties of the sequence, i.e., cyclic and inductive. By the examination of the computer program, it is proved that every two-times sorting sequence falls onto a periodic cycle with the cyclic length 1, 2, 3, 4, 5, 6, or 12.},
 pages = {48--55},
 publisher = {情報処理学会},
 title = {Every Two-times Sorting Sequence Falls onto a Cycle},
 volume = {2001},
 year = {2001}
}