## [問題]有趣問題

### [問題]有趣問題

10, 11, 12, 13, 14, 20, 22, 101, 1010, X
請問 X = ?

chinhsi

1,2,3,4,5,6,7,8,9,10 .............................................10進位
1,2,3,4,5,6,7,8,10,11..............................................9進位
1,2,3,4,5,6,7,10,11,12............................................8進位
1,2,3,4,5,6,10,11,12,13..........................................7進位
1,2,3,4,5,10,11,12,13,14.........................................6進位
1,2,3,4,10,11,12,13,14,20.......................................5進位
1,2,3,10,11,12,13,20,21,22,....................................4進位
1,2,10,11,12,20,21,22,100,101................................3進位
1,10,11,100,101,110,111,1000,1001,1010................2進位
1,11,111,1111,11111,111111,1111111,11111111,111111111,1111111111
................1進位

10=11=12=13=14=20=22=101=1010=1111111111

(1)10,10,11,10,11,100,10,11,12,101,10,11,12,20,110,10,11,12,13,
21,111,10,11,12,13,20,22,1000,10,11,12,13,14,21,100,1001,10,
11,12,13,14,20,22,101,1010
, 10 ,11,12,13,14,15,21,23,102,1011,
10,11,12,13,14,15,20,22,30
(規律同上面的解釋,由進位法所得,但不包括1進位)

(2) 1,10,11,10,11,111,10,11,100,1111,10,11,12,101,11111,10,11,
12,20,110,111111,10,11,12,13,21,111,1111111,10,11,12,13,20,
22,1000,11111111,10,11,12,13,14,21,100,1001,111111111,10,11,
12,13,14,20,22,101,1010
,1111111111,...
(規律同上面的解釋,由進位法所得)

(3)10,11,12,13,14,20,22,101,1010,1111111111
(原題,也是2號數列的一部分)

http://www.research.att.com/~njas/sequences/indexchinese.html

J+W

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